planning a veg plot

My veg plot is around 16ft long and 8ft wide the right hand side north left hand side south, on the "south" side is a plum tree, not overhanging the veg plot too much but still casts a bit of shade underneath, also it is more damp than the rest of the plot, is there a crop that would manage to survive these conditions and/or what could I do to improve the soil condition - the further "north" you travel up the plot the better the soil, its like breadcrumb at the top and just right. thanks in anticipation!

 

Little d you could add lots of manure, compost etc. to try abd improve this part of the plot. Potatoes and brassicas may do well in this part and the potatoes will help break up the soil.