They are too young to manage their own money and spending at the moment, so you don't need normal bank accounts for them yet.
Firstly, do you want savings for when they are 18, or savings for now to buy more expensive pressies for them, or savings for their pension?
If you want to save to when they are 18, you should open junior stocks and shares ISAs for them. Invest in a couple of global tracker funds for each of them and put money in each year. This will grow exponentially by the time they are 18 and they will have house deposits when they leave home
If you want short term savings (perhaps useful when they are 10+ and want to buy a computer game, clothes, a new Xbox etc) then you can add savings pots to your own account (we do this on Chase, just name another account after my son and he can save into that), this way they can earn interest on the savings.
Or you can use Rooster with Natwest - it's free if the parent has an account. They will be able to use it when they are older and you can keep track on the app. But there's no interest on a Rooster account.
Finally, did you know you can open pensions for your kids - you can put in £2880 per year and the gvt give them a tax rebate, grossing it up to £3600. You don't have to put the full amount in each year, but just a little will give them a next egg to build on when they get their first jobs, and they can start adding to it without having to think about how to set up their own.