Plants that will grow in clay soil

List; Climbers, shrubs, ground cover & herbaceous perennials that grow in clay soil.

Aster. Great cut flower, From miniature alpine plants to giants up to 6 feet tall, there are over 250 asters, with plenty of colors to choose from. Asters are a great way to brighten up the Autumn garden.
Butter daisy. With its demure veil of jewelled blooms, coreopsis adds charm to cottage gardens and formal flower beds alike. Dainty flowers, thin stems and fine foliage disguise the fact that this plant's as tough as nails. It's also great for cutting and readily attracts butterflies.
Day-lily. This garden favourite  seems to grow anywhere and does well in clay soil

Fern. Ferns are so versatile. You can find a plant for just about any growing condition...sun, shade, even  clay.
Japanese iris. Japanese Irises are among the most showy and easiest to recognize of all garden flowers. It's also one of the most common beardless irises, which are generally easier to grow and more adaptable than bearded types. 

Potentilla,  By the time many other flowering shrubs' colourful show is over potentilla is just beginning its long flowering season. It is one of my favourites because its blooms will last until the first hard frost and it will grow in clay. 
Virburnum. My favourite ornamental shrub for three reasons - it's beautiful, it's versatile, and it's easy to grow in clay.

And even vegetables for the kitchen.
Runner bean. The runner bean is a twining climber, which is great trained up a trellis. This vegetable is fast-growing and will attract butterflies to your  garden. 

Trees and shrubs to grow in clay soil.

Trees that will grow in clay soil. Acer japonicum, palmatum (Japanese maple), Amelanchier lamarckii AGM, Betula (birch), Cratageus (hawthorn), Eucalyptus, Laburnum anagyroides, L. x watereri 'Vossii' AGM, Liquidambar styraciflua, Malus (crab apple), Pyrus salicifolia 'Pendula' AGM (weeping pear), Sorbus

Conifers for clay.  Araucaria araucana, Chamaecyparis lawsoniana, C. obtusa, C. pisifera, Ginkgo biloba AGM, Juniperus chinensis, J. x pfitzeriana, J. virginiana, Picea abies, P. glauca, P. omorika AGM, P. orientalis AGM, P. pungens, Pseudotsuga menziesii AGM, Taxodium distichum AGM, Thuja plicata, Tsuga candensis, T. heterophylla AGM

Shrubs that will tolerate clay. 
Buddleja, Cotoneaster (evergreen and deciduous), Escallonia (evergreen), Fuchsia, Hydrangea, Mahonia, Rosa, Spiraea, Viburnum (deciduous and evergreen), Weigela

Ground cover, Climbers and Herbaceous perennials for clay

Ground cover for clay soils. Bergenia, Euonymus fortunei, Gaultheria procumbens AGM, G. shallon, G. x wisleyensis, Geranium, Hypericum calycinum, Juniperus communis, J. regida subsp. conferta, J., horizontalis, Lamium galeobdolon, Persicaria affinis, P. bistorta, P. vacciniifolia AGM, Rubus pentalobus, Vinca major, V. minor

Climbers and wall shrubs to plant in clay soil. Chaenomeles x superba 'Moerloosei' AGM (pink) and 'Nivalis' (white), Cotoneaster horizontalis AGM, C. lacteus AGM, Forsythia suspensa AGM, Escallonia 'C.F. Ball', E. 'Edinensis' AGM, Garrya elliptica 'James Roof' AGM, Hydrangea anomala subsp. petiolaris, Kerria japonica, Lonicera japonica, L. periclymenum, Pyracantha, Rosa

Herbaceous perennials that like clay soil. 
Alchemilla mollis, Anemone hupehensis var. japonica, A. x hybrida, Aster novae-angliae, A. novi-belgii, Astrantia, Geranium, Helleborus, Hosta, Kniphofia, Sedum spectabile AGM Solidago 

Essential minerals for health gardening Explained here minerals for heathy soil

 follow this link for: How to breakup and improve clay soil.