With such a small space I'd advise you try to keep plants coming through in pots ready to plant out as soon as something is removed, also be prepared to import a lot of compost or manure... if your soil is acid then mushroom compost is good if you can get it, if you're growing intensively then you need to look after the soil a bit more, also look out for crops that give good productivity for a small space.... if you can get a frame up on the northern edge of the plot then runner beans or climbing french beans will give tons more beans than any number of dwarfs, and over a longer season. Same goes for climbing (tall) peas... you could have four feet of Cobra beans, four feet of Telefono peas and a couple of "Black Forest climbing courgettes... lots of produce, not much footprint.... I'd also target stuff that is always better homegrown or really fresh, strawberries (I'd always usually suggest soft fruit, but not in 10x10), grow them in tower, move them in front of the climbing stuff once that's got going and only plant up one side, the stuff facing north won't crop that well, shallots from seed, poncy salad mixtures, garlic for green garlic, all sorts of small cabbage, though minicole and hispi are pretty good, you can have pots with the winter savoy Wintessa ready to go in when other stuff comes out, also some leeks, maybe even some brusells (way better fresh than shop bought) and witloof chicory.. If you love sweetcorn then you could grow a small patch, you could get 20 plants or so into a 4x4 space, you might well get away with planting one of the shorter climbing early-cropping shelling beans in amongst them... Bridgewater or Polish CLimbing would make sense, avoid Borlotti, it takes too long.... I can let you have some Bridgewater or polish though.. To avoid wasted space start most things off in modules is a good technique, especially if you can do it at home, seedlings are fragile and they're a lot easier to look after in module packs.... even things like carrots adn parsnips if you stick a toilet roll tube into each cell of a 24-cell module pack (I'd debate growing parsnips, but having two or three in for Christmas dinner might float your boat)
Stuff to avoid... probably potatoes aren't worth the effort, cauliflowers take up a lot of space and time, most pumpkins and squashes, though if you must grow one then Winter Festival is about as good as you'll get, it's pretty compact and will give you four or five sensibly sized fruit that store well. Onions unless you have a hankering for something odd, if you must grow one then Long Red Florence tastes great adn it's tall thin bulbs allow you to pack them in a bit tighter than normal ones in the flat...
