Some of the answers already given make me say
Yes....but...
Shopping online with a delivery pass. Well, yes, but if you can stick to your shopping list, and if you pass a supermarket (no extra petrol), you would save the cost of the pass.
Online if you use
http://www.mysupermarket.co.uk/ you can find the cheapest shop for your basket, and they tell you if another brand or size would save money.
Once you have saved a bit you can buy extra when things are on offer then next time buy less/none of that, more of that weeks offer.
If you shop near closing time there may be bargains BUT ONLY buy what you will use before best use by date.
Don't throw away things just because they pass their Sell By date, use your common sense. Tins are OK for years unless dented or bulging. Veg & fruit are OK if they look OK, and may still be edible if slightly shrivelled. Meat can be dangerous if not stored carefully and fats go rancid and don't taste good, so be careful with those. Use older things first, put new shopping to the back of the fridge/cupboard.
Bulk out leftovers with veg and make another meal.
I agree that some Own Brands are as good as names, some not, so try everything once. If you can't tell the difference, keep buying it, if you can decide if it's worth it.
Think about your spending on entertainment. There are dear nights out and cheap nights out or in. It will depend if your friends want to save too, and how strong willed you are if they don't - let them know you are trying to save and limit the meals out etc either by going less often or by suggesting a cheaper alternative.
Writing down everything I spent and balancing the books weekly worked for me when we started out - I still keep records but less detailed. Because I don't impulse spend 'saving the change' wouldn't work for me. Some people find that giving themselves so much cash a week and that's it - no plastic - works. For others once a note is broken the change is frittered, so plastic and keeping accounts works better.
So you need to think what would work for you. When do you spend most.
Good luck.