Any organic matter including spent mushroom compost and garden compost, also 5ml grit. This is something you will have to keep doing for a while to open up the clay.

Agree with MG's answer - humus rich materials, as much as you can load on and as often as possible, which would include composted animal manures from the garden centre, leaf mould, plus the ones already mentioned, anything like that and some grit.

If you can buy (or get for free) well rotten horse manure that will work well. Perhaps add a little grit along with it.

This rings a bell as we are on really heavy clay. As above anything organic helps, even just laid on top it will eventually work it's way down with insect/worm help and any weeding you do. We have a really helpful professional tree person who dumps his wood-chippings here and we pile them around the bottom of the hedges to keep them weed free. Cheaper for him to dump here and free for me, but this won't work if you are choosy as you get all sorts! Won't work on a small garden either, but perhaps a local sawmill has sawdust/shavings waste, horse manure is usually cheap or free. Time is actually the major thing about working clay, time to add and time for it to work! Otherwise - give up and grow things that like clay - roses do!