The best thing you can do is improve your soil. In the autumn, add a generous amount of soil improver (like Vitax 6x or similar) - that will break down the clay over winter and improve the soil quality. Also consider adding a thick mulch of compost or bark clippings so your soil retains humidity and stays at a more constant temperature.
That said, lots of plants are perfectly happy in clay soil. Shrubs like Cotinus, Fatsia, Sambucus nigra, salix mount aso, Nandina all do well in clay in shade or semi shade, and shrubs are generally low maintenance and can provide year round structure and interest. Lots of perennials would work too - if looking specifically for shade, Polemonium, Bergenia, ferns, periwinkle, pulmonaria, clematis to name just a few. Astilbe corms are cheap (often 2 for £2 at Morrisons) and they grow quickly if planted in the spring.
I think wild flower mixes tend to work better for sunny areas rather than shade.
Growing from seed can be challenging and slow going, especially in the shade. Lots of plants require warmth to germinate so need to be started indoors. If you can afford it, I’d buy potted plants to get started. Even the 9cm perennial pots will be considerably bigger by the end of the summer and they will look great next year. Shrubs are even more rewarding, the small plants you put in this year could be six foot tall next year.
Just make sure you buy plants that are pest resistant. For instance I have zillions of slugs and snails, so hostas are a no go. Also avoid things that are super invasive. I would never plant bluebells as they will take over everywhere. Or euphorbia as they’re hard to get rid of. The RHS website has lots of useful information.