Planting in heavy clay soil can be very challenging as it can be a chore to dig over in summer when it resembles concrete or again in winter when it is very sticky. For the gardener it is always advisable to try to improve conditions of clay soil by digging in plenty of organic matter along with some coarse grit and use plenty of mulch on the surface of the soil, planting in late winter or early spring to minimise waterlogging. When planting, having dug the hole or trench it is always advisable to break up the base of the hole with a garden fork to assist with drainage as otherwise it can act like a sump and retain water which may rot the plants.
Clay soil is full of nutrients and will sustain quite a large range of hedging plants from Native Hedgerow Mixes including Quickthorn, Hornbeam, Field Maple and Wild Crabapple to the more ornamental plants for informal hedges such as Mock Orange, Snowberry and Forsythia or Viburnum Tinus with the pretty leaf colour, flowers and berries. For evergreen hedging in clay soil you can do no better than the superbly majestic English Yew, fast growing Thuja Plicata Atrovirens, or for security cover as well as evergreen there is the thorny Pyracantha or the slow growing prickly Holly. Lonicera will also tolerate clay soil and with its tiny evergreen leaves and tight structure provides a dense impenetrable structure which can be clipped to a tidy formal hedge.
As with all gardening good initial preparation is the key to a fruitful end result and this applies more so with clay soil since in the beginning you may have limited days when you can actually dig the ground.