Does anyone have any knowledge about a good children's savings account? I'm looking for something safe, that pays a good interest, and remains in the control of the parent although in the name of the child (so tax free for the child).

First look for a good savings account then ask the question about putting it in a child's name. Better banks and building societies should say "yes". You should be the signatory for the account until the child reaches 18. Alternatively, use the Money > savings options from the top menu to look for accounts that are specifically described as being for children.

I used the option from the top menu as you suggested and found a Halifax account with 10% interest for one year, thereafter, the balance gets moved into another account annually. I guess it depends on what the interest rates of that other account is - more research to do.
Thanks for your advice.