UK banks are paying savers “measly” rates on their cash even as the Bank of England has taken its base interest rate to the highest level in more than a decade, according to a study from the consumer group Which?.

Consumers face rates as low as 0.1% for some instant access savings accounts, Which? found.

That appears particularly low when compared with the Bank of England’s key interest rate, which was set at 4.5% in May. This is the highest level for the central bank’s base rate since 2008, in the height of the global financial crisis.

Such a high interest rate at Threadneedle Street made the “measly rates” on offer to savers “unjustifiable”, Which? said.

Consumers may be better off switching from their high street bank in order to get the most attractive rates, it added.

“With millions of consumers still feeling the impact of an unrelenting cost of living crisis, it’s become even more important to get better returns on savings accounts,” said Jenny Ross, the editor of Which? money.

“Yet, our research shows that established high street banks are shortchanging customers by potentially hundreds of pounds a year.”

In February, bosses of some of the biggest high street banks were quizzed by MPs on the Treasury select committee about why rates on savings accounts were so low.

Last month the City watchdog, the Financial Conduct Authority, said it had also warned some banks it might make “onerous interventions” if they did not pass on higher interest rates to consumers’ savings accounts.

UK Finance, a banking lobby group, has challenged some of the criticism levied at banks, saying that there is more to the interest calculation for savings accounts than it might seem.

The Bank of England’s key interest rate is only one factor when working out what rate to offer on a savings account, according to a blog by Eric Leenders, the managing director of personal finance at UK Finance.

“Other factors include the cost of raising funds, both in the retail and wholesale markets, capital and liquidity requirements, customer and regulatory expectations and the fact not all borrowers will fully repay loans,” Leenders said.

Still, the introduction of a new FCA “consumer duty” , which comes into force on 31 July, may trigger a clampdown on those banks who are not offering fair rates to consumers – but only if it is “worth the paper it’s written on”, Ross said.

There are also some new savings deals on the market for those consumers who are prepared to switch banks.

First Direct is set to launch a one-year fixed-rate savings account with a rate of 4.60% AER (annual equivalent rate) on 30 May.

The deal is only available to First Direct customers with a First Direct current account. The bank is also offering £175 to switch to its current account, subject to terms and conditions.

Last week, Shawbrook launched a one-year fixed-rate bond paying 5.06% AER and a one-year fixed-rate Isa at 4.43% AER.

A UK Finance spokesperson said consumers should consider whether they needed instant access to their cash or could deposit funds for a long time when hunting for deals.

“While the interest rate on an instant access account may be lower, they offer customers the flexibility to access their money when they need it. The market is competitive, with a range of fixed and variable rate products available,” a spokesperson for the lobby group said.

“We would always encourage customers to shop around for the product and interest rate that is suited to their needs.”