Mature hedges should be cut back at the start of the growing season in March or in Winter when most hedges lie dormant. Dont wait until temperatures start to go up because that's when the sap starts to rise & any hard pruning could cause stress to a hedge. Do not cut back hard leylandi Cyprus or Conifers as they will not rejuvenate from old wood & could even die. You can reduce in height the top will bush out eventually from sides growing & spreading upwards. Conifers should only be cut after any frosts have gone & no later than the end of August or beginning of September.Beech, yew, hawthorn, privet, holly, pyracantha, escalonia and cotoneaster hedges are good examples of hedges that can be cut back hard in Spring.Dont cut both sides of the hedge in one attempt. Cut one side one year and the other side the next or this could weaken or kill it. Always use sharp and clean loppers to give a neat finish on thick stems that a hedge trimmer cannot cut through & to prevent disease. Make the hedge around 8 inches wider at the base than the top to allow light to reach the base encouraging growth.You can put fertiliser and compost at the base to feed root system afterwards to encourage new buds to grow from the bare stems. When new buds get a few inches long then lightly trim to encourage shoots to spread & branch out.
Before working on a garden hedge please check there are no birds nesting, as Under the Wildlife & Countryside Act 1981 it is an offence to damage or destroy a nesting site of any bird while its being built or in use.