Big banks are now paying top rates on easy-access savings accounts with deals over 4 per cent – but you won't find them on their own websites or in their branches.

Instead, you must ferret out the brand names they operate under. 

NatWest has a new digital savings brand called First Active; Barclays savings accounts are offered through Tesco Bank; for Santander it's Cahoot; Lloyds accounts are under MBNA; and top-paying HSBC accounts are offered by savings platform Raisin UK.

Finding these secret accounts can earn you £350 more in yearly interest on £10,000 of savings than traditional accounts – and sometimes pay three times more.

NatWest launched an Instant Access Savings Account through its First Active brand last week, paying 4.5 per cent on as little as £1.

Link it to your current account (which doesn't have to be with NatWest) to move money quickly and easily, with no limit on the number of withdrawals.

By contrast, on NatWest's own-brand Flexible Saver, you get just 1 per cent on up to £25,000, and while its Defined Access Saver pays 2.5 per cent, this falls to 1.04 per cent after three withdrawals in a year.

You can only open the First Active account online and you can't open a joint account. Make a diary note to switch after a year when the bonus rate of 1.5 percentage points runs out.

HSBC has joined savings platform Raisin UK to offer an Easy Access Account paying 3.51 per cent with no bonus or withdrawal catches. Accounts on HSBC's own website pay far less, though.

Its Flexible Saver pays 1.05 per cent and while its Online Bonus Saver pays 3.35 per cent, in any month you make a withdrawal it falls to 1.05 per cent. 

Barclays offers good rates through Tesco Bank. Its Internet Saver pays 4.21 per cent, including a 3.16 percentage point bonus for a year, so again mark your diary.

That compares well with just 1 per cent on its Barclays Everyday Saver and 3.9 per cent on its Rainy Day Saver – on up to £5,000. This falls to just 0.7 per cent on anything more.

Santander pays 4.52 per cent through the Simple Saver account run by its offshoot Cahoot. 

Again switch out after a year or you'll end up earning just 1 per cent. Even so that's better than on Santander's own Everyday Saver, which pays just 2 per cent (falling to 0.9 per cent after a year).

So far Lloyds only offers a lousy easy-access account through its offshoot MBNA paying 0.75 per cent.

But it has a great one-year fixed-rate bond at 4.85 per cent against just 3.8 per cent on its own website.

Ultimately, these new accounts are good news for the millions of savers who want to stick to big names for what they see as reasons of convenience and safety – even if other providers offer exactly the same level of both.

Such savers have missed out for years on interest because the big banks pay truly awful rates on standard, easy-access accounts.