These are accounts that are shut to new customers and often – but not always – pay lifeless returns. Rates have been known to fall to as a low 0.05%, which means you would earn a pitiful 50p a year on a £1,000 savings pot.

The general view is that once banks and building societies have lured in customers with headline-grabbing rates they turn all their attention and resource into attracting new business.

The number of “zombie” accounts in the market is far from insignificant.

According to Which? Money, there are 1,952 instant access and notice savings accounts and cash ISAs, but only 390 are open to new savers’ deposits.

Some 607 of these accounts, Which? says, pay just 0.5% or less in interest. And 258 pay 0.1% or less.

Halifax Liquid Gold, Barclays’ Savings Builder and HSBC’s Instant Access all pay the worst rate of 0.05%.

Worryingly, savers appear to be in the dark about “zombie” accounts, despite the fact that in the current record low interest rate environment, they should be making their money work as hard possible.

Research by RateSetter found that 79% of Britons admit to not checking their savings returns against inflation, while over half – 52% – don’t know what return their savings account is currently giving them.

Rhydian Lewis, RateSetter founder and CEO, said: “Zombie accounts are doing hard-working savers a real injustice. We want to help the public realise this problem and show them that there is a positive alternative to savings accounts, which will give them a fantastic return on investment. Given the economic climate, it’s never been more important to make the most out of our hard-earned money, so we hope our zombies will shock people with ‘infected’ accounts into action!”

If you do find yourself in one of these “zombie” accounts, earning a pittance, the advice is vote with your feet.

“Move your funds to another account – either with the same provider, as they can often have similar accounts paying better rates, or with another provider if they are offering a market leading account. Unfortunately if you want to make your savings work hard for you, you need to stay vigilant and don’t let inertia win,” says Anna Bowes of Savings Champion

Some of the worst “zombie” accounts: