Not specifically children's but the hairdresser at Transit Way has special children's seats (a duck and a rabbit if I remember correctly!) and toys. They seem to have on hairdresser there who is particularly good with children too, I'm sure they've mentioned that to me before. We've always been pleased with them.
Thanks for the Maiya recommendation. They were absolutely fantastic when DD (3) found a pair of scissors and made herself 'look like a bridesmaid'. They turned a Mel Gibson, Mad Max style mullet into a sweet little bob. And still only charged £5.