This sounds like a really fun
project. It is a size that you can not only do initially but keep up with; I'll bet you end up with more out of your little garden than many a large plot that has gotten away from its owner.
After making a few gardens (and tons of mistakes over the years!) in a in a cool maritime climate, I suggest currants, runner beans, edible-podded peas, and greens as the screen plants and main crop. These are likely to be the heaviest-bearing and most reliable for where you live. Now that I garden in the lower 48, I can grow tomatoes, beans, sunflowers, cowpeas, but for years those things were just a wistful dream. On the other hand, the growth of salad crops and cooking greens in maritime climates is endless, and over the winter you should be able to have lots of cabbages, Brussels sprouts, kale, and so on. If you prepare your soil well at the start, you could eat out of your garden a lot. I love planning gardens --used to do it for a living for awhile--and I've sketched out a plant to give you 100 square feet of growing space and adequate access for harvesting.
Perpetual Spinach (a chard here; called leafbeet there) should be a perfect crop for you, probably perennializing for at least 3 years. Rhubarb lives forever and will grow in some shade. Welsh onions would make a
perennial clump and likewise live for ages. Other perennial vegetables take a while to establish, and are often low-yielding. (I'm thinking of seakale, artichokes and asparagus, which probably don't provide enough of a harvest to pay their way in a small garden.) The area at the base of that high fence is likely to be in shade much of the day. You could put rhubarb, Welsh onions, and perpetual spinach there, or train red currants (which don't take as much sun as black currants and bear on older wood, so can be espaliered) on that fence. Spinach, parsley, and lettuce will take some shade and could also be grown in that area, if you leave a section for annuals. All of these are available from Bountiful Gardens in the US and online, or from Chase Organics in England. Perennials are often available as starts also.
I would put a 2-foot wide, very well-amended bed along that fence for your shade-lovers. Then a similar 2-foot wide, very fertile bed along the low fence--half for peas, and half for runner beans, which are very heavy bearers in a moist climate (they don't pollinate well where it is very dry). Alternatively, put herbs along the low fence and beans trained on a
trellis at the gate end. Either way, you have a long sunny bed along that low fence.
Depending on where your gate is, I would run your main path along one of those beds. Even though you are trying to save space, I'd make a 3-foot wide path if it is going to be used daily to get anywhere. You don't want to to feel like you are walking a tightrope every time you come and go. Allowing a narrower path for access along the other bed, (say 1 1/2 or 2 ft wide) you still have room for a nice wide bed in the center where the sun is and where you can have access from both sides for cultivating and picking. How to Grow More Vegetables by John Jeavons will be helpful here.
If you put salad stuff, Asian greens, and brassicas like kale in that bed, you will have all the greens you can eat all summer and a couple days a week in the winter. Chard (leaf beet or silverbeet) in particular offers the most meals per square foot of any plant I know. Other possibilities are roots like carrots and beets, and broad beans or winter peas in winter for a spring crop. Add some herbs in pots or along that fence between you and the allotments, and you have a very productive garden that will be dependable in your climate. I can recommend a couple of
books, both written in England: The Self-Sufficient Gardener by John Seymour, and Salad Greens for all Seasons by Charles Dowding. (Dowding makes a living on a quite small parcel selling salad greens.) They are both really, really useful and good reading.