noshed is right about cucurbits - they thrive on lots of muck. it's common to make heaps of manure, cover with a light leaf mould then top dress with compost - cucurbits will love it.
if the ground and muck is lumpy then root veg will probably struggle your spuds will be ok but not great and greens will be fine. beans like a drop of the rich stuff as does celery. my toms are in large wooden troughs and have a good helping of manure at the bottom.
if you put in plenty of muck, your plot is less likely to dry out and if there was straw in it - it should help to break down the clay.
i would just avoid long rooted veg.
good luck