Sorry but I think you will struggle to find anywhere for less than that. Actually, I think the norm for a ladies cut and blow dry in London is between £ 40-50 !! Is it worth looking for any colleges that offer hair dressing courses that are looking for models - that might be free/ cheaper than £ 25? Alternatively, many hairdressers have model nights to train their juniors - often they advertise in their windows for models so that might also be worth s shot? Good luck!
Groupon often does hairdressing deals but I don't know that you'd get much below £25. Never tried them myself, so there may be all sorts of hidden stuff I'm unaware of. Might be worth checking out though.