Forsythia - you'll lose all next year's flower if you cut it now. Should be done after flowering, mid-spring latest.
Berberis, if it needs doing, but, again, you'll lose next year's flower. It's a late spring/early summer job, after flowering, depending on which species you have and when they flower.
Laurel and privet, useful hedging shrubs, and evergreen, aren't usually cut after about August. If cut later, especially where you are, any new growth (which they are provoked into producing by being trimmed) is likely to get hit by the first frosts of winter and damaged. That's a general (but not hard and fast), rule for evergreens.
However, all that said, if the shrubs NEED reducing for some reason, then the berberis and forsythia won't suffer much, both being very tough. The laurel and privet may suffer some damage, but if healthy, will both recover easily enough next spring.
Hope that helps

Well-written and useful, detailed answer !
I've added to GoYpedia Pruning :o)

Thanks very much Hortum_cret for your very useful information. I arranged for someone to come weeks ago to do the job, but they have kept putting me off due to bad weather interrupting their other commitments.

I think the best thing I can do is tell them to forget it for this year. Thanks again.