Agree with ajol. I think it's called a smart account. Good rate of interest. Dd1 has two of them. One with a cashcard - I transfer money online to her account so she can pay for trainfares etc, and another with a book for savings.
Have been doing a bit of research since I posted this and came up with the Nationwide a/c and the Halifax a/c (plus the Halifax regular saver one - excellent 10% rate, even if it is only fixed for one year).
Good to have positive feedback on the a/c which looked one of the best, so thanks.
The 10% Halifax one is a right faffle. I went to set one up each for my 3 dds. You have to have feeder accounts so in all I did paperwork for 6 accounts. It worked for a month then they closed 2 of the accounts as there was no transactions for 30 days. It was their mistake but to get the feeder/10% account combination going again would have meant me filling in 4 application forms again (for "security purposes"). I just closed the remaining 2 accounts because it wasn't worth the hassle.
There is a limit on the amount you can put into the 10% account as well - it's really low.
Second (or third!) Nationwide. Not always a chart-topper, but consistently good interest rate, and don't do that maddening thing of having a headline-grabbing rate and then quietly dropping it once they've pulled in loads of business.
Do remember that your child's account will only be tax free if the money in it came from someone OTHER than the parents. If it came from you, the IR deems it to be your savings and you must declare interest for your tax. (And they make you prove it too, so keep records of all of granny's cheques!!!!)