I opened a child's Stocks and Shares ISA for my little one when they were born with Hargreaves Landsdown (they don't charge much in terms of fees). I have found it the most efficient way to save for long term, if that's what you're after.

http://www.hl.co.uk/partners/search/junior-isa?theSource=PCMBJ&Override=1&adg=AD+HLBJ+JIS&utm_source=adCenter&utm_medium=cpc&utm_campaign=HL Brand - Junior ISA PCMBJ&utm_content=HL Stocks Shares JISA PCMBJ&utm_term=hargreaves%20lansdown%20children's%20isa

Do you mean (a) a child savings account where you put money away for your little one or (b) a child bank account where the child can use the funds eventually and treat the account as their own? I am opting for (a) right now, and opening a child saving account for my one year old. It is attached to mine, kind of like a Cash ISA account. You need to apply at your bank and they have different requirements to open one. For example, HSBC needs to see a copy of the child's birth certificate. If you are opting for (b), then you should look at a website that compares children's bank accounts like which.co.uk:

http://www.which.co.uk/money/banking/bank-accounts/guides/best-childrens-bank-accounts

Keep in mind however, that there are minimum age requirements for certain child bank accounts. If your child is very young, then a saving account attached to your own account might be the best option right now if you are just looking to put money away.

I am interested too. :D

Can anyone recommend a child bank account please with the interest rate, I am going to open an account for my little one, she's 3 month old now but I don't know anything about it. Thank You