what shrubs for shade and clay soil

How tall do you want the plant to grow? For winter interest try Helleborus orientalis or Arum italicum 'Pictum'. Or the Japanese painted fern Athyrium niponicum. These all do well in my garden which is also on clay. Make sure that you dig a good hole (mind the trees roots) and add some compost to enrich the soil. Water all summer as the tree will take a lot of moisture out of the soil. Coloured leaves may be better than flowers in the shade although spring colour is easy, try Pulmonaria, snowdrops, Leucojum (spring snowflake).

Mahonia aquifolium if you want something about 3 feet and evergreen, bit slow growing though. Ajuga reptans doesn't mind the dark, though it doesn't like the dry, and is just ground cover. Geranium varieties, lamiums, brunnera, pulmonaria ditto.

on the egde of the canopy line i grow fuchsia and phygelius. Or there is pittisporum and eunonomus [spelling?] that will tolerate some shade. Aucuba too will manange.