Some advice

[THE_Liam]

The log book, as already stated, isn't proof of ownership, just that of the keeper so the DVLA know where to send the fines lol.
I have had experience of this (although not to purchase a specific product but to pay an ex debt) I ended up in small claims court.
My best advice would be to save and print off any text messages relating to the loan that you have from her.
Copy of your monthly statements showing that she has paid you regularly, a regular amount.
Speak to the garage and see if you can get a copy reciept of purchase as technically you are the owner.
Get a copy of the loan agreement and the balance to pay.
Write her a very polite letter including all these things, post it to her, stating you want to do it amicably, once she's paid she wont hear from you again, and if she hasnt replied with a solution or payment, you'll seek FURTHER legal advice (she doesn't know you haven't) bla, bla, bla. At the same time do yourself a copy, sign the back of your copy of the envelope (along with a respected person if you can), tape over the seal and signature then post it to yourself. Include in yours a letter stating that you posted hers on the same day. Its important that you post both copies as the date stamp is proof of date. (It stands up in court).
If you get no reply IN WRITING from her after the 2 week deadline, take legal advice from there.

Ps... I got my money back.

This is brilliant advice!