In reply to JamButty:
Having just been through all this, with my own car at the age of 23:
I got cover as a learner through a specialist insurer, Acorn. Really good to deal with, straightforward on the phone, friendly UK call centre, good prices (£95/month fully comp, as the only driver on that car, as a learner). If it had been someone else's car who had it insured independently, probably would have been less - however some insurers don't like people having temporary policies on "their" car so be careful.
Price is likely to be slightly higher, on the hand, as I presume your daughter is 17-19. However learners are a pretty good insurance risk compared to newly qualified drivers in the same age bracket.
That's the way I'd do it, so I'd advise you look into it.
Stewie