When i was that age, about 7 years ago, i had the Nationwide Smart Account, you can opt only to have the book.
I did this because if i had the card i was more likely to dig into it, i left the book with my mum to look after.
The interest rate is 5.27 AER on ever pound in the account.
I remember getting lots of vouchers and coupons when i opened as well. which was helpful, cos it had money off thorpe park and chessington and over theme park.
It seems to evolved since with the online account managment.
Personally, from experience i found this really useful, and they can upgrade your account to the flexaccount when she turns 18.