It depends how willing your friend is to live frugally, or whether she expects a certain standard of living and London 'experience'.
You could do it for £200/wk without the unnecessary entertainment, and doing other things for free (museums, sights, galleries etc), making your own lunches, going out to cafes not bars.
That would mean the 5 inclusive months she is here could be done for less than £5000. Any money she has beyond that she could budget for her 'entertainment', rather than just wasting it on spontaneous going out, which always racks up more cost than intended.