First of all if you are on a budget it is not the time to follow fad or restrictive diets. Paleo, keto, velocity diet etc. These tend to be very expensive while results can be achieved following more regular food choices, an even mix of macros and watching your calories.
Learn where to shop. There are many budget supermarkets out there such as Aldi and Lidl which tend to be cheaper than the regular big supermarket names. There are also frozen food specialists such as Iceland and Farmfoods. Farmfoods especially is full of loads of cheap nutritious food so if you have one locally check it out. Amongst the bigger supermarket chains Asda appears to be the cheapest with Waitrose being the most expensive. Sainsbury and Tesco seem to be in the middle. By all means shop around for particular items as prices may vary amongst supermarkets.
Now let's look at each macro and go over the cheapest and best sources available
This is going to be your most expensive macro and the most important. Evaluate protein sources based on the grams of protein per £ spent.
If you are really on a budget and you need protein then just eat the cheaper conventional meat and eggs rather than organic, free range or grass fed. Let's be honest the difference between the two is minimal and if you are on a tight on money protein is very important. Now you might not ethically agree with it but unless you are vegetarian and outside the factories with a picket line I doubt you actually care about aminal welfare as much as you think you do. I expect a massive load of hate and butthurt for putting that. Try to eat less fatty meats such as chicken, turkey and lean mince beef. One of the main benefits of grass fed meat and free range eggs is the better ratio of omega 3 in the fat. By eating less fat you are avoiding the worse ratio from conventional meat anyway. I'll get to how you can improve the fat ratio later. Also the majority of toxins from meat are stored in the fat so this also helps you reduce those which maybe in the conventional meat.
The cheapest meats tend to be chicken, turkey and beef mince. Chicken and turkey thigh is even cheaper than the breast. skin on is cheaper still and you can always remove it later.
Buy frozen if you can. Frozen chicken breast, chicken thighs, frozen mince, frozen fish fillets are all just as good as the fresh versions but much cheaper. When it comes to fresh meat turkey and pork are your best bet and you can get mince from both at a good price. Casserole meat can be cheap and great for stews and soups.
Eggs can be cheap if you get regular ones but even the free range ones aren't too much more. I've found 6 eggs for 70p yielding around 45g of protein.
Tinned fish. Frozen white fish is fairly cheap but some really good sources are tinned. Tuna and salmon are the most obvious ones. Salmon even when tinned is still quite expensive while tuna is a cheap and good source of protein. But less common fish are also very cheap tinned. Mackerel, sardines, pilchards and anchovies are all fairly cheap tinned. These are also pretty high in omega 3. If you eat these often enough you can push your omega 3 ratio quite high with no worries about the fat you've been getting from conventional meat and eggs. You can even avoid the need for fish oil supplements. Just make sure you get them in brine or olive oil. Even tomato sauce. Just avoid getting them in sunflower oil as this is so high in omega 6 as to defeat the object of eating these.
Liver and other organ meats are some of the most nutritious foods you can eat and is also some of the cheapest. A 400g liver will cost you about £1 for around 60g of protein and a massive hit of almost every vitamin and mineral. It may not be that tasty so you might have to play around with cooking methods and recipes. Personally I can just eat it fryed with some onions and veg. You won't need to spend money on multivitamins if you eat this a couple of times a week.
Cottage cheese is an old bodybuilding favourite for its slow release protein it's also very cheap.
While not a complete protein source kidney beans are dirt cheap and full of vitamins and fibre.
Finally protein powder. You may think this isn't exactly cheap but that's because you buy it by the kilo. Depending where you get it from this could be anywhere from £15 to £30. Avoid GNC and buy it online from bulkpowders or myprotein. if you look at the grams of protein per£ you'll actually realise that's it's very cheap indeed.
Here's a quick run down of some of these foods from a protein g/£ ratio most of these are from ASDA online
Smart price Turkey breast 33g per £1
Turkey thigh mince 45g per £1
Farmfoods beef mince 33g per £1
Pigs Liver 225g per £1
Smart price beef and pork mince 69g per £1
Frozen chicken breast 40g per £1
White fish fillets 40g per £1
Farmfoods eggs 60g per £1
Large free range eggs 27g per £1
Tinned tuna in brine 45g per £1
Tinned mackerel 30g per £1 with 4g of omega 3
Tinned sardines in brine 46g per £1 with 4.4g of omega 3
Cottage cheese 30g per £1
Myprotein unflavoured whey 53g per £1
Myprotein flavoured whey 44g per £1
Kidney beans 40g per £1
These are just are just a few examples obviously prices may vary so you'll have to work out your own ratios.
As you can see liver beats the rest by far but you can't eat that stuff day in day out. Some are better than others But it's good to get a mix of sources for a more balanced amino acid profile and for the sake of taste variety.
Carbs tend to be pretty cheap as it is and are not usually a worry. The cheapest sources without being complete crap are porridge oats, rice and potatoes with tinned potatoes being especially cheap at about 20p a can. You can get oats and rice in kilo bags for around £1. Whole grain pasta is cheap and so are rice cakes for snacking potential. Even whole grain bread isn't very expensive. Don't worry about gluten or paleo as chances are you can digest gluten just fine. And don't have the budget to be really fussy. Rice and potatoes are gluten free though. You certainly don't need expensive carb powders Like dextrose or multidextrin for post workout. Any carb source will do.
You can certainly get some of your fat intake from your protein sources. Most other fats tend to be more on the expensive side especially the healthful monounsaturated kind.
For saturated fats you have single and double cream if you simply need the calories also full fat Greek yogurt. Coconuts are quite cheap at less than a £1 for a whole one. They have medium chain triglycerides with many health benefits. You can drink the water for a good source of minerals and electrolytes as well.
You can get creamed coconut which can be used to make coconut milk as its cheaper than buying the milk ready made. Peanut butter is fairly cheap and a good source of monounsaturated fat but avoid other nut butters as these are very expensive.
Nuts themselves are generally not that cheap but the most bang for your buck comes from almonds and walnuts. Buy them unsalted. For cooking use regular olive oil. Butter can be used in some cases as well. Olive oil is not cheap but is your best bet. Vegetable or sunflower oil are too high in omega 6. And the paleo favourite coconut oil is massively expensive as well as unnecessary since the healthy fats can be gained much cheaper from an actual coconut.
Vitamins, minerals and fibre
Here I'm talking about fruit and veg mostly. You can get a lot of cheap veg frozen with all of the vitamins and minerals remaining locked inside. Frozen broccoli, peas, mixed veg, peppers, stir fry mixes, cabbage and spinach. Can all be picked up for around £1 for a big bag. Starchy veg like parsnips, turnips, Swedes and potatoes tend to be less nutritious so you may be better just have a cheaper carb source like oats or rice. Red onions can be bought fresh and are more nutritious than white ones. Generally more colourful veg is better than white veg so I don't bother with cauliflower, Swedes or things like that. Salad leaves and lettace are pretty void of nutrition so don't waste your money on those. Tomatoes can be bought tinned and are actually more nutritious when cooked like that. They work great with mince dishes. When it comes to fruit berries contain the greatest amount of antioxidants. In summer when they are in season they tend to be fairly cheap but at other times of the year you can pick up frozen mixed berries quite cheaply. Blend them in smoothies or have them with yogurt or cream. Of other fruit apples and bananas are well priced and ignore the more exotic fruit from half way around the world.
When you are on a budget you really need to be critical of the supplements you take. Looking at the g/£ of protein ratio you can already tell that whey powder is actually cheaper than alot of food so I suggest keeping it in your diet. Beyond that nothing else is really necessary. Omega 3 can be obtained from oily fish so you may not want to spend money supplementing there. Vitamins and minerals can be obtained from liver and lots of fruit and veg. So a multivitamin is not needed. Creatine is a very cheap supplement that can actually make a big difference so if you can spare the money it can be worth taking. If you need a boost pre workout then pick up some caffeine tablets such as pro plus rather than fork out for expensive preworkout supplements. It's mostly the caffeine which helps you anyway. Every other supplement has questionable scientific evidence to back them up and really aren't worth your money.
When it comes to beverages obviously you should mostly drink water. If you need some taste then go for sugar free flavoured waters rather than the typical big brand diet soft drinks. They are far cheaper. Tea green tea and coffee will just have to be budgeted for if you need them.
Buy in bulk. You can save money getting bulk deals and multipacks. Most people get paid on a monthly basis yet shop weekly. For non perishable items you can shop emphasising bulk deals when you have more money in order to save more. What deals are available depend on the supermarket so look around.
Check out the discount section and fresh food counters. Supermarkets usually discount perishable food which Is going out of date by as much as 75% for the last day. You can pick up some real bargains on meat and fish. Usually there is a certain time of the day that these products are reduced so try to find out when this is so you can pick up a bargain before anyone else does.
If you are bulking a great way to add calories is to drink a can of evaporated milk. It will set you back about £1 for 600 calories with a fairly even mix of fats carbs and protein. It even is quite high in vitamin D. But don't confuse this with condensed milk which is much higher in sugar. A very easy way to bulk would be to just drink a can of this in addition to your regular meals for that 600 calorie surplus.
Learn to use spices. While not cheap if you only buy one a month it is not much money. Some of these foods are very bland so may need spicing up a bit.
Pay attention to calories and macros when eating on a budget. You can use one of the online calculates to find your customised amounts. This ensures that you don't over eat and spend money needlessly and by having a balanced carb intake allows you to have some very cheap food sources rather than the more expensive proteins and fats. You can even emphasise more calories from carbs and have a lower fat intake. This is not necessacarily a bad thing as some people fair better with higher carb intakes and have more energy. As long as your calorie intake is in check you will not get fat. This applies to bulking cutting or maintaining. Don't worry too much about meal timing either just focus on getting the carbs fats and protein you need over a 24hour period.
Don't cheat too often. The foods I've outlined are very cheap compared to pizza, ice cream, cookies, eating out etc. If you cheat quite often the money soon adds up.
Avoid processed diet foods which are always very expensive. Gluten free bread and cereal, protein bar's, sugar free chocolate, and similar things available in most health food stores.
You can save money from food also by fasting. The typical intermittent fasting protocol of 16 hour fast 8 hour eating is no good since you will still eat the same amount of food. But a once weekly 24hour fast can have numerous health benefits but I won't go into them here. It can work well if you are cutting and save you an entire days worth of food. But do not exceed one day a week for this and don't train that day.
Finally see what you can get for free. Depending on where you live you may be able to hunt and gather a little. This may be a bit crazy but you never know what's out there. I know in my local area at certain times of the year there is seafood mussels, cockles, and winkles, seaweed, blackberries, chives and nettles. There are also lots of wild rabbits. I'm sure there is plenty of protein right there.
Finally I've give you a few cheap meal ideas
Oats with whey protein and skim milk
Mince meat of choice with onions chopped tomatoes, kidney beans, garlic salt and rice
Stir fry liver, chicken, onion, mushrooms and assorted veg
Soup from assorted veg potatoes and skin on chicken thighs. Remove the bones when cooked
Defrosted mixed berries with double cream
Weightgainer smoothie with evaporated milk, whey protein, banana
White fish with chives cooked in butter with mixed veg and rice
Rice cakes with peanut butter on
Mixed veg omelet
Simple meals like these are all very cheap. Eating like this might not be the most tasty or exciting way to eat but when you have a tight budget you need to focus on quality nutrition. At a guess I would say it would be possible to have a weeks food at around 3000 calories a day with balanced macros for about £40-50 taking into account bigger buys at the start of the month like protein powder.
While it might not be the absolutely healthiest way to eat. When it comes to making progress whether muscle gains or fat loss it will achieve the exact same results as any grass fed organic gluten free extra virgin natural free range diet will.