Lots of good suggestions already, especially opening up the soil with organic matter, the more the better. I've gardened on Wealden clay for over 40 years. You specifically asked for perennials. To what's already been suggested I would add the primrose family; cowslips do well for me. Surprisingly some alliums do well and seed, also geum, hellebores, marjorams and sedums. Roses and to a lesser extent honeysuckles especially like the clay. There is so much you can grow; just avoid the things that really don't like the wet.
Based in Sussex, I garden to encourage as many birds to my garden as possible.
Fantastic to hear about the astrantias @Bright star many thanks! I'm surprised at the sedum but pleased as it's another low maintenance easily divided and self seeds... win all round! Thank you @Redwing
Achillea, Spirea, hellebores, verbena and, surprisingly, Mexican fleabane have all done very well on my slightly sloped clay bed since I inherited it last spring. Ferns are loving it too.
Not perennials, but if you are interested in a bit more if a cottage garden feel, I have a few fruit bushes dotted between the flowers in my border in heavy clay soil in full sun which are doing great. I especially like the honey berry, it starts flowering in March before the leaves are fully developed which adds a bit of nice early spring colour. This year feverfew has been self seeding around the garden and I rather like it, it kept repeat flowering right up to the end of December but some might consider a bit invasive.
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I'm surprised at the sedum but pleased as it's another low maintenance easily divided and self seeds... win all round! Thank you @Redwing