We can get it to work but have to modify it a lot where we live.
I have two approaches, I add compost, well just about any organic material I can get hold of, sawdust is good, but I also hoe all the balls of clay that accumulate into a corner of the bed and pick them up, they then go in a bucket in the greenhouse to dry out, and every time I have a bonfire a couple of bucketfulls go into it. It produces a sort of coarse terracotta, then I put it through the riddle to separate the ash and smaller bits and smash the larger bits up. Most of it goes into potting compost, but of course it all ends up in the garden eventually.
I do quite like a bit of clay though, if I am filling pots for something like planting broad beans that will get planted out I will put some clay into the compost, break up the lumps and mix them in. It holds water and nutrients in a way that compost doesn't, in small quantities it is a good thing, but it is easy to have too much of a good thing.
The first people here must have tried using pebbles underneath the soil for drainage, the neighbour tells me they imported a lot of mushroom compost many years ago, but over time the pebbles have simply embedded into the clay below. The last person to live here for fourteen years took no real interest in the garden, just had a man in to mow lawns and cut hedges every so often, I estimated I found a heap of about 3.5 cubic meters of old cuttings piled at the end of the garden, that helped. People recommend sand, but I don't find that works well at all, the silica is too heavy I think.