I'm a bit late to the party, but I agree that investing in a stand alone fridge is an excellent idea. There are 2 of us, and we do a £50 monthly protein/bread/canned goods shop - taking advantage of bulk deal buys and free delivery from either Waitrose or Sainsburys - and freeze it all. Once you by online, the supermarkets will send you emails with deals like £10 of your next shop when you spend £50 - that sort of thing, trying to keep your business.
Then during the week I'd pop out to buy the dairy, breakfast and other essentials at a combination of local greengrocers, Sainsburys and Whole Foods and spend about £20/week. Of course this is not including wine or any eating out, of which we probably did about once a fortnight. So our shopping budget for 2 worked out to between £30-40 per week.
In order to keep in our stringent food budget, I did have to lower the standards of what I might buy, but the milk stayed organic and I tried to stay as sustainable and local as possible. That being said, Sainsbury's basics are fantastic value - I've compared the ingredients to more expensive items and they are the same, sometimes healthier. Plus I learned how to cook all sorts of things to keep stuff interesting, like risotto, thai curries and savoury pies.