Our place is a bit wet and soggy too, although we are further south. As we were digging over the ground we collected all the rocks (lots of rocks) and used them to build up the edge of 20ft x 6ft veg beds. We then use some additional soil and compost from local recycle place to build up the bed 6-8inches above the ground level. It keeps it drier and seems to help a lot.
I would try potatoes, carrots, leeks, beetroot, broad beans and some herbs. Jerusalem artichokes for a little exotic flavor although they give you wind. Peas may work, or if weather looks rubbish eat the shoots in salads. Lettuce, radish, and perennial onions should be OK too.
Brassicas like alkali soil so don’t do well, too cold for runner or green beans.
Have a go at lots of stuff, look on internet for smaller packs of seeds so you can experiment