Several actions you can take, preferably doing all of them:
1. add lots of organic matter, such as well rotted manure. You will need a lot more than you will get from your compost heap. Not only is it a good fertilizer, but it also conditions your soil, which means it stops tiny clay particles from clagging together, which is important for drainage in winter and moisture retention in summer.
2. Add lots of sharp sand. Not builders sand, which has salts in it which can harm plants. This improves drainage and makes the soil more workable.
3. Add lime or gypsum. The chemistry is complicated, but this conditions the clay soil like organic matter, stopping clay particles from binding together. Lime will make your soil more alkaline, so if you don't want this then use gypsum, which has no effect on soil acidity. Buy builders plaster, which is practically 100% gypsum (except colouring) and is a lot cheaper than horticultural gypsum.
You can get sharo sand and plaster from your local merchant. And whatever amount of manure, sand and gypsum you think you are going to need, treble it!! You can't add enough, and its a lot harder to work in more after you have planted up.
I used a rough ratio of 6:3:1 manure, sand and gypsum. I have found a local horselover who collects horse manure from her paddock by hand (gloved!) so no straw - 50p a large bag!!!!!.