It does take a bit of turning around Digger 1957, but I would say the easiest method is to cover the ground liberally ( a good 8 to 10 inches of manure) and leave it for a growing season. If its weedy cover it with thick cardboard first, then manure it.....removing any perennial weeds, you can leave the annuals they will add more organic matter as they rot down.
Make sure the ground it wet before you do this. This summer is ideal, as its soooo wet!!
Come next spring, chuck another thick layer of well rotted manure on top, and plant potatoes through the layers of manure into the soil. Cover and let them grow. (tatties are great for breaking up hard ground. I apologise if you already know that)
You will be amazed how the clay improves, do this every year and you will have gorgeous soil. This is no dig gardening which allows the rotting of the manure and the worms to do all the hard work for you. It also keeps compaction of the ground to an absolute minimum, very important on clay.
You could also try raised beds using compost and manure to fill them, or the same as above. Keep one bed free and use it to make your own compost for next years crop!
This is my personal preferance, but its up to you wether you want to dig or not. Hope this has helped. Good luck.
