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Lloyds TSB and Nationwide had pledged to pass on the reduction to their standard variable rate (SVR) customers before the Monetary Policy Committee announced the change, while HSBC will also be cutting its SVR by the full amount.

But other major lenders were slower to respond to the change, saying their rates were under review.

Peter Bolton King, chief executive of the National Association of Estate Agents, called on all major lenders to pass on the rate cut.

He said: "The fact is that without the major lenders passing on this cut, and without stronger commitment from the Government to fully address the problems of the housing market, this cut is practically an exercise in spin.

"The MPC and the Government continue to pat themselves on the back while hardworking families across the country increasingly fear for their futures.

"What is particularly frustrating is that it is evident that there is a pent-up level of demand among first-time buyers that, if released, could provide the stimulus needed to kick-start the housing market.

"If the major lenders commit to passing on this cut, and the Government suspends stamp duty, we could open the door to recovery."

Lloyds, which also lends under the Cheltenham & Gloucester brand, and Nationwide had little choice but to cut their SVR, as they pledge that their deals will never be more than 2% above the base rate.

The reduction will leave both groups' SVR at 3.5% from February 1, while HSBC's will fall to 3.94%.

The move will save borrowers with a £150,000 mortgage around £40 a month, while those who are more heavily mortgaged with a £250,000 home loan will be around £68 a month better off.

But the majority of lenders are not expected to pass on the reduction in full, with some warning that they need to balance the interests of their savers with those of their borrowers.

Savers, who vastly outnumber borrowers, have been getting an increasingly raw deal since interest rates first began to fall, with more than a third of accounts for deposits of £5,000 now paying interest of just 1% or less.

The problem for banks is that they need to continue to attract savers' money in order to fund their mortgage lending due to the shortage of funds in the wholesale money markets.

The key inter-bank lending rate, three-month Libor, continued to fall today, dropping to 2.5% ahead of the announcement that the base rate was being slashed to 1.5%.

The rate, upon which many variable rate mortgage deals are based, has fallen by around 1.3% since interest rates were last reduced in December, to stand just 0.5% above the base rate before the latest cut.

But despite the lower borrowing costs, the majority of lenders are expected to pass on only half of today's reduction to both new borrowers and those on SVRs.

Just over half of the UK's 11.7 million households with a mortgage have a fixed-rate deal and so will not benefit from today's reduction.

A further four million have a tracker mortgage, while just under one million are on an SVR.

But around 300,000 borrowers with tracker deals will not see their rates fall as so-called collars will have kicked in, meaning lenders no longer have to pass on the cut.