Well it worked mate.
Plugged in the adaptor and tried the epilator after 10 mins and it worked so it seems that the problem lies there. For now she'll be able to use it now simply by just plugging it in a few minutes before she needs it. In the longer term I'll have a look around for similar adaptors and see if I can find something suitable lying around or buy one.
The details are:
Pri: 100-240v ac, 50-60hz, 7.5w.
Sec: 13v, 400ma.
I can't see anything on the adaptor regarding the polarity of the tip so do I assume it doesn't matter?
Replacement Philips epilators of this quality aren't cheap so even buying a new adaptor might be justified.