CLAY SOIL

I don't suppose there is any one best plant.. And perennial is very vague? What characteristics do you want?

Here are some ideas:
http://www.crocus.co.uk/bomcard/_/perennials/other-perennials/verbena-bonariensis/classid.2000008597/

sorry i cant help im a new gardener dont really no much but i mixed composs in mine and grit and chicken pellets my plants seem to like it ,i was just worried for the drainage but after putting these things in the clay/soil its ok now

Hostas are great for clay soil and come in different leaf colours and flower well in the summer. Another great plant although more of a shrub is Rose of Sharon or the smaller form evening primrose oil plant. Both have wonderful yellow flowers all summer and grow well in very poor or clay soil. The smaller forms are good for ground cover and die back in the winter. Mine are just starting to sprout leaves from the base again and are in very bad clay soil! The larger shrub is great for the edge of a garden or if you want a bigger feature plant, again this dies back in the winter but is worth it for the flowers during summer.

Hi there
I have very poor clay soil and have grown the following quite well: campanula, Jacob's Ladder, Marguerites, verbena bonariensis, agapanthus, lambs ears, penstemmons, foxgloves, red valerian. Shrubs that are doing well so far are: ceanothus Yankee Point, buddleia, forsythia, lavatera, hawthorne, Himalayan Honeysuckle as well as jasmine and honeysuckle climbers.
I'm trying a few more this year but those above are growing in very heavy soil that doesn't get much sun and is quite clogged and covered in moss too.

Hope this helps :-)