As above, don't be a brand snob! Own brands are usually fine and a big saving.
Don't buy jar or packet sauces, make your own. You can make a big pan of a tomato based sauce and freeze what you don't need so it is as convenient as a jar next time you want some.
Be aware that cheap washing powder/washing up liquid/loo roll isn't always the most economical buy as you use much more.
Beans, lentils and lots of veg are your friends.
Meat free days make a big difference. Quiche, omelettes, frittata are good meals. Cauliflower cheese, macaroni cheese also good. Remember you can serve them with salad or veg.
If you have to make sandwiches, don't buy packet ham. Buy a small gammon joint, boil it and slice for sandwiches. Cheaper and nicer. Again, freeze some in useful portion sizes.
If you buy a chicken, then buy a big one and make it stretch. There are lots of threads on here about rubber chickens!
Look at your portion sizes. Most of us(me) use far too much protein in a meal which is better replaced with more veg.
If you have a family that likes to snack then make your own. Cake, biscuits, flapjacks, brownies plus savouries such as cheese twists with puff pastry.
Look at the FB page 'Feed yourself for £1 a Day' .. you won't want to go to those extremes but there are some great money-saving ideas on there.