What part of London are you in and how far are you willing to travel?
Anything in central London is going to be more expensive, but you may find if you travel out to more residential areas in Zones 3/4/5 you could probably get something cheaper.
The place I go to in East Finchley is a nice "normal" salon. Not overly posh, but not catering to the old blue hairs (if you know what I mean....).
It's called TD Hair Designers and I think the woman who has cut my hair, could probably do up-dos. Her name is Tanya.
T D Hair Designers
170a, High Rd, London, N2 9AS
Tel: 020 8883 5777
It's only about a 5-10 minute walk from East Finchley tube station. I think a cut is £25-30, so fairly reasonable. Good luck!