Politicians and consumer campaigners have been heaping pressure on British lenders to raise rates for savers as fast as they have hiked rates on mortgages, as an intensifiying cost of living crisis is particularly acute for poorer households.

The FCA said it had seen signs of progress from lenders and encouraged savers to shop around for better deals.

"We now want to see that progress accelerate," the body said in a statement.

Sheldon Mills, FCA executive director for competition, said in a broadcast pooled interview that he believed savers were getting value when taking into account the full range of products available.

"It's not for me to set rates for banks," Mills added, after a meeting with nine lenders, including Britain's 'Big Four' banks - Barclays (BARC.L), HSBC (HSBA.L), Lloyds (LLOY.L) and NatWest (NWG.L).

The watchdog's moderate tone may disappoint critics. Lawmakers on the influential Treasury Select Committee on Monday accused banks of "profiteering" from customer reluctance to switch to products with higher rates.

"While it's welcome to hear the banks recognise further action is required, it’s time to see an acceleration in progress," the committee's chair Harriett Baldwin said after the FCA's meeting with banks.

"We will be following developments closely and will be particularly alert to any apparent foot dragging."

Britain's finance minister Jeremy Hunt has also said banks have been too slow to pass on higher base rates to savers.

David Postings, chief executive of bank lobby group UK Finance, said the savings market was competitive and lenders offered a range of different options for savers.

The Bank of England has raised benchmark rates to 5% - the highest since 2008 - and investors are betting in money markets that rates could hit 6.5% by early next year.

Despite this, the average rate on an instant access savings account was 2.49% as of Tuesday, compared to rates above 6% on two-year and five-year fixed rate mortgages, Moneyfacts said.

Banks have said they are increasing saving rates, particularly on fixed products that lock up customer cash for a certain period.

"Convenience is costing savers who keep their cash stashed in an easy access account with a big high street bank," said Moneyfacts' Rachel Springall.

Rocio Concha, director of policy and advocacy at consumer organisation Which?, said it was unacceptable that some banks were failing to offer competitive savings rates.

"While it is true that consumers can shop around for a better deal, they should be treated fairly by their bank whether they switch or not," Concha said.

"The regulator must continue to hold banks' feet to the fire to ensure they do the right thing."

The roll-out of a new 'consumer duty' later this month requiring banks to demonstrate how they are treating customers fairly will give the regulator more leverage, lawyers say.

Mills said that a forthcoming FCA report on savings due at the end of July would address data privacy restrictions that constrained banks' communication with customers on rates.