We preferred Marks & Spencer for the best variety of 'grab and go' grocery store options.

Pretty much every museum, garden, national park, etc. will have a cafe for lunch options. Will run from £4 or so for a mediocre cellophane-wrapped sandwich (if you're in the realm of that kind of thing, go for the panini version when possible. The better bread does make a difference) to £8-£12 for a full lunch, often made in-house from regionally produced meat and produce. And sometimes in a really lovely setting like the Orangery at Kew Gardens or the Museum Cafe at the Victoria & Albert.