Hi Thanks for the advice. My version of XP is legitimate. It came pre-installed from a reputable dealer and I ran the tests you suggested.
Strange thing is that all the updates have now installed !!!!! My daughter was using the PC and when she powered it down it offered her the option to install them - so she did.
I've checked via Add/Remove programs and Microsoft update and they're all installed. I've tried to install the optional "Update for Windows XP (KB904942)", but this failed in the same way as the others did.