Great advice from Kristen.
I'd also suggest climbing french beans (start them early and plant out in June- they take a little longer to start cropping, but give a long cropping period and prolific.... French beans are more expensive than runner beans to buy, and well... i'm pretty partial to them, particularly the less stringy varieties.
Things like Kohl Rabi are pretty quick growing, and Pak Choi, you could succession sow them well into late Summer.
And when you havent got the floor space- use the wall space? Cant see how high your other wall is but you can get nice trailing varieties of cherry tomatoes for hanging baskets... or put a trellis/support along the wall and grow an outdoor ridge variety of cucumber?
Succession sowings of lettuce can keep you in salads all Summer and will mean you're continually harvesting- which feels nice when you're starting off. And there are some decent iceberg/crisp head lettuces that will outsmart (and out flavour) the rather expensive supermarket varieties? (And they wont wither in the fridge... just pull a few leaves as you need em!!
Spring onions I think are more space effective than regular onions, which are cheap to buy... You can get varieties that 'bulb' up a little too... just thin them as you pick and the later harvests will be more 'onion like'.
Turnip (not swede) grow fast and can succession show for a long time.... better use of space than swede that sit there for a year growing at snails pace? You can buy turnip varieties that are a double crop as they produce v tasty leaves too (cook like cabbage or kale... steam it +knob of butter, crack of pepper.... mmm)
I also got a good crop from Kale- i grew Nero di Toscana from realseeds... they are 'cut and come again' (like a lot of Kales i believe?) When you harvest the Kale, cut it instead of pulling it, just below the head... and leave the stalk with about 3 or 4 fair sized leaves still on it in the ground.... it will then sprout 3 or 4 more heads.... so you get another harvest before the spring.
(and its hardy, so you can leave it growing all winter)
Use intercropping!!! Sow your radish in between your rows of Kale (for eg) when you're sowing... the radish will get harvested in 6 weeks, just at the point where your kale starts to need the space. A neat thing about doing that is the affect on flea beetle... i was growing some japanese greens and kales that flea beetle will happily ruin... but they far far prefer tucking into radish... they go mad for radish!!! So they attack the radish, leaving your other leafy veg alone (and they eat the bits of the radish you probably werent too interested in anyway? (Though i still use mine for radish top soup... no-one will ever know those leaves were riddled with flea beetle holes!!!)
Rocket is another great fast fast growing one thats great for intercropping- and ridiculously expensive in the supermarkets given how little time it took to grow it, and the fact that its well.... leaves?!!
Perpetual spinach is another 'all year round' cropper. I presume it slows down in the winter? I grew it this year for the first time... i didnt like it... its like chard. If you like chard, you might like it... Its a member of the beet/chard family so... not actually a spinach (but waaaaay easier to grow)
And how about a strawberry planter?