The soil here is solid clay too. When I arrived there were a couple of beds that hadn't been used for a while, but were distinctly better than the rest, the next door neighbour told me that the people before last (Fifteen years ago) had a huge pile of mushroom compost delivered, but I have also created a couple of beds where there was nothing before and it was solid clay.
People are down on clay, but it has useful properties as well. Those tiny particles get a ball of water around them which holds dissolved nutrients. On its own, not so good. My additions to it are any and all vegetable material I can get hold of, my new bed I first of all dug out large squares and simply turned them over to bury the grass and weeds and expose the clay. Exposed like that over winter it does break down to a degree to something which much more resembles soil. I have a large oak at the end of the garden which sheds leaves and twigs like mad. Oak does not break down easily, and I bury all that stuff as a sub layer. I collect the small balls of clay that accumulate whenever I rake of hoe, and whenever I have a fire in my incinerator in they go. I break the resulting terracotta up into something like sand, except that it is lighter and permeable, or add the larger pieces to the base layer to help drainage. I find sand is not a good additive other than in small quantities, despite it being recommended, too heavy and solid. On top goes all the compost and other vegetable matter I can lay my hands on.
It takes time, but over a couple of years I have created a couple of quite decent beds where there was solid clay right to the surface.
You will always do better in the soil than out of it. I think it is the fact that humidity and temperature don't vary so much or so rapidly. I have found that with the things I grow in pots for the summer and then move into the greenhouse if I dig a shallow hole to put them in and then use the spoil to fill in in-between the pots to make a single lump of them everything does much better.
My other bit of advice is 'Don't go mad at it', start off with a single small bed and gradually expand year on year. That way the additions are more concentrated and it is not a huge task that just looks impossible. Then grow something like climbing beans that are going to add nutrient and all their root system to it the first year, runner beans (lima beans?) are quite happy with new compost in quantity, I actually empty the compost bin from the kitchen straight in the hole on top of the twigs and leaves just before covering and planting.
Once the bed is going I keep mulching.
Solid clay can become some of the best soil there is.
