Go for a bike which is Full Cro-mo I'd say. Mine was £200 second hand (decent frame with average parts) and I've gradually upgraded it as I've gotten more and more into it – perhaps spent about £250 more on it since I got it.
I'd recommend speaking to Stodgy (Dave) at http://www.radBMXshop.co.uk – tell him I recommended speaking to him and I'm sure he'll look after you even if it is just giving you some good advice on what to get.
He's a top guy and always willing to sort people out with bikes that are right for them rather than just selling anything to anyone. Give him a call.
Another good site to browse is http://www.sourcebmx.co.uk – their site is better laid out that most with lots of glossy pictures and shiny things to tempt money out of your wallet.
My list of bits to look out for are:
Full Cro-mo frame and fork
3pc cranks
Micro gearing (10-28t or 9-25t) especially if she is going to ride park – makes it easier to get over the coping – this includes a cassette hub).
Chrome rims (especially back)
Brake (rear only is fine)
Right size frame for someone her height)
Nothing too heavy – mine is about 26lbs
A bike around the £300 mark will have most of this on, if you spend more you'll get more but this is about the price point where bikes get good.
There is a difference between a park and race bike (I won't mention Dirt and Flatland) and it really comes down to what she wants to use it for.