If size is an issue and she really isn't bothered about gaming on high graphics settings at all then a NUC or equivalent might be worth looking at, obviously you severely limit the upgrade paths for the system.
http://www.amazon.co.uk/Intel-BOXD54250 ... 00ID4HSBY/Remember you have to put that with a HDD (1TB ~ £50), memory (8GB ~ £50) and a copy of Windows (around £80 for a retail boxed copy) if required.
EDIT - And just in case it isn't clear, if she isn't bothered about size you can get much more for your money by getting a regular sized PC.