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/ba ... k-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.