....although obviously supporting local farmers is great!

Have you considered raised beds? Our soil is also really heavy clay; pond-like in the winter and completely compacted in the summer. We built some raised beds using an old divan bed base as a frame and then old bits of wood to fill in the panels. I’ve seen some done using old tyres stacked up. Or large pots?

We don’t grow a lot but manage lettuce, tomatoes, spring onions, carrots, radish, peas and broad beans. It’s a wonderful thing to be able to wander out (into our city pocket handkerchief size garden!) and pick food. It fair makes you feel at one with the land!