what flowers grow well in clay/ not too good soil in UK.?

I think I'd get a load of compost or well rotted manure and fork it in all over to a depth of about a foot at least. This would have the effect of improving drainage, improving air movement and helping to prevent that drying out and cracking you get with clay. That will increase the number of plants you could give a go. You might need to experiment to see what 'does'. If it were me, I'd go to the garden centre and get a load of packets of seed of reliable flowering annuals such as marigolds, poppies, nigella, sunflowers, Lychnis coronaria and scatter onto the prepared ground. Don't know where you are in the UK, but if you are not too far north then a good perrennial you could try is a hardy Osteospurmum, which will provide groundcover with pretty silvery daisies.

Calendula does really well for me as does Cosmos and Centaurea. Liatris, Echinacea, Coreopsis, Eryngium (sea holly), Leucanthemum (Shasta daisies), Monarda (Bee balm), Rudbeckia, hardy geranium, Hemerocallis (daylilies), Sunflowers, poppies, roses of course, Cerastium tomentosum (Snow in summer), Peonies, Echinops.....all grow well in my heavy clay soil.
Dig in as much organic matter as you can. Make sure you mulch the soil surface with some kind of organic material at least an inch thick. This will help prevent the cracking you get with clay and also help stop the clay from compacting quite as much. It will also encourage worms into the soil which will help with the compacting and aerate the soil. Spirea, Lilac, Buddleia, Philadelphus (mock orange) and pines are also doing well in my soil.