The bank’s MySavings account for children aged 7 to 17 years old will pay 3%, up from 2.75%, on savings up to £3,000 and it can be opened with £10.

Santander’s Mini 1 2 3 current account also pays 3% but on balances up to £2,000 and the minimum opening deposit is £300.

The HSBC rate is available to new and existing customers from 3 September.

For children (or parents) wanting an account, which allows immediate access to their money, this will be the top deal.

But higher rates are available if you or your child can save regularly.

Halifax Kids’ Monthly Saver pays 4.5% for 12 months. It requires a monthly deposit of between £10 and £100 and withdrawals are not allowed.

Saffron Building Society’s Children’s Regular Saver offers 4% for 12 months and a maximum of £100 can be deposited each month. This account is easy access so you can withdraw your money at any time but it can only be opened and managed in branch or by post.

Tom Adams, head of research at independent savings advice site, Savings Champion, said: “It is also worth remembering that you can save for your child tax free with a Junior cash ISA – Coventry Building Society currently tops the table at 3.50% tax free/AER (rising to 3.60% from 1 September).

“You will need to bear in mind that with a Junior cash ISA, access to your money is restricted until the child reaches the age of 18, although you can transfer between providers if you see a better deal.”

Top children’s easy access accounts (correct as of 20/8/18):