Bed with varying light conditions - how to use shaded area

Hi there guys
I have just moved into a new flat, and it has a lovely, big patio with a 4x1m stretch of soil at the back, so I am hoping to start my first fruit and veg garden. I found this soil does reach deeper than a spade, although it is extremely rocky. The soil quality is on the sandy side, but as I can't afford all the new soil + compost I'd need for proper raised beds, I've decided to strain as many rocks as I can out and use them to create borders so I can raise the beds just slightly, and improve the existing soil with however much compost I can get my hands on.
The problem is, the patio is west facing, and this bed runs along the west wall, so a third of it is sunny, a third is partially shady and a third is in full shade. Furthermore, the buildings all around it add to the problem. I'm fairly confident I could grow raspberries, cauliflower or some herbs in the sunny corner if I build the soil enough. In the partially shaded bit I am thinking of peas, french beans, broccoli and maybe some lettuces. I am stumped though for what to do with the shaded bit. The soil is more waterlogged here, and I don't want to dump loads of compost into it if it has no chance of growing anything anyway. Will leafy greens grow in full shade, so I can have a little salad bar here? I also have a little gooseberry plant that I'm training at the moment, I heard gooseberry does well in full shade. If I keep that potted until it's bigger, and then plant it in the shady corner, would that be a solution?
Of course I am also using plenty of containers and vertical solutions on the sunny north and east walls, but I want to make the best use of all the earth I have here, any suggestions would be much appreciated.
Here are some pictures to illustrate the problem and show the soil quality.





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The furlong bit confuses me - a furlong is over 200 metres
but we'll presume you've got a reasonable depth of soil 
I once had a very similar garden to yours. I grew runner beans, lettuce, swiss chard, courgettes, various herbs and strawberries in the ground and tomatoes, dwarf french beans, carrots, beetroot and tomatoes in containers.
Because of the lack of direct sunlight in much of the garden except in mid summer I tried to find varieties that produced an early crop - that worked quite well.
Get some bags of well rotted farmyard manure from the garden centre and dig it into the soil - it'll be fine
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
I edited that hahaha, no idea where my mind was going at the time!
That's great to know that you could grow all these things, and early varieties are the ones I have invested in so that is great.
My gooseberries were in the woods and grew very well... Slower but bigger fruits... Beetroot also grows well in shade as do pumpkins and courgettes. I grew all of these In my raised beds which are in the wooded part of my garden with great success... We also grew asparagus that did well
Thank you for your tips, Stacey! I have that little gooseberry plant... it's just a little wee thing at the moment so I'll pot it up and wait till it's a little bigger to put near the shady area.
I also had the idea of possibly putting a mushroom log there!