Have the same problem as you where I live (15m south of B'ham). that bad in fact that when I dug a pond, after one spades depth of crap soil I hit solid (patchy) clay, realised I probably didn't need the liner I had brought. What I do now is for every three spadefuls of soil add a scoop (two hands full) of sharp sand or "garden" grit + a shovel full of recycled compost from local authority (they used to be called councils, what happened while I was away? I wouldn't give them authority !!) and another "handfull" of pea grit if available and give a good mix/chop up. Breaks it up nicely and we have palms, agave, bananas etc. etc. doing quite well.
Another alternative is a load of horse muck in autumn, had this at my last house and the next years lawn was the greenest I had ever seen (we had toooo much and what do you with a pile of sh*te ?).
Scoby