It's very doable.
Aldi/Lidl for shopping for basics and household stuff. Markets, if you have one, for fresh veg and meat.
Get a slow cooker! There are cheap ones for about £15. Cheap to run and fantastic for producing large amounts of soup/stew/chilli etc etc without effort. The smells when you walk in from work will offset any 'poor' ingredient issues and cheaper cuts of meat will tenderise beautifully.
I manage two adults and a four year old on about £30 a week for food, and we're not eating boring, plain pasta every night or jacket potato and beans.
For example, it was Katsu curry last night (I made the coating for the chicken pieces and the sauce from scratch. Served with rice, it cost about £1 per person). It's chilli tonight, chicken provencal tomorrow and probably soup on Wednesday, to use up all the bits of veg etc I have left lying around before payday. I used half the mince packet in the chilli tonight earlier in the week to make sheppy pie.
The trick is seasoning and lots of tinned and frozen beans and veg and pulses. The dreaded Iceland do a roasting veg mix that has baby onions in it - just lovely in soups and stews and it lasts for ages!!
Pancakes can also be your friend. We don't use them much here except once a year, but... Get a cheap mix, make the pancakes, put grated cheese, chicken, veg, whatever in the middle, roll them, put them in a baking dish, cover with more cheese and bake. Lovely, and filling, and quick. A decent alternative to potatoes and pasta as a carb base, as well.
When things have been really tight, I can bring a fortnight's shopping in for three under £40, but that's not something I'd want to do regularly, as it wouldn't be healthy. £25 a week for one person should be perfectly doable.
The trick is to have fun with it, be creative, try new things. Challenge yourself!