Prime Minister Gordon Brown says the government has met lenders to urge them to pass on the cut in interest rates.
He said the Treasury and the Bank of England had acted to help lenders and now banks should take the lead.
Chancellor Alistair Darling held a breakfast meeting with bank bosses this morning to press the government's case.
The Bank of England's official rate was cut from 4.5% to 3% on Thursday. The Libor rate at which banks lend to each other has fallen since the cut.
The first two lenders to respond have been the Nationwide building society and the RBS/NatWest group.
The Nationwide is cutting its base mortgage rate by 1.5%, from 6.19% to 4.69%, while RBS/NatWest is cutting its standard variable rate by the same amount, from from 6.69% to 5.19%.
This follows similar moves by Lloyds TSB and Abbey on Thursday.
"We are determined to get banks to resume lending," Mr Brown said.
Chancellor Darling met the banks at the Treasury, and the banks attending were thought to include Abbey, Barclays, HBOS, HSBC, Lloyds TSB, Nationwide, Royal Bank of Scotland and Standard Chartered.
'Commercial decision'
The Council of Mortgage Lenders (CML) said lenders would cut their rates by between 0.5 and 1.5 percentage points in the coming weeks.
The problem banks have got is that they have limited funds and don't have enough money to give to all the customers who may want them
However, the CML warned that the precise level of the reductions would be a commercial decision for each individual lender.
Michael Coogan, director general of the CML said: "The problem banks have got is that they have limited funds and don't have enough money to give to all the customers who may want them.
"I think over the next few days and weeks we will see that the banks and building societies will move by anywhere between 0.5% and 1.5% - the individual decisions will be on the basis of assessing what they want for their savers as much as what they want for their borrowers," he added.
These cuts would be for existing customers on standard variable rate (SVR) deals, with deals for new borrowers likely to be re-priced.
Almost all tracker mortgages have been withdrawn for new borrowers as lenders consider at what rates to reintroduce them.
Duty
Conservative Party leader David Cameron said that banks that had taken part in the government's bail-out programme should be forced to pass on Thursday's interest rate cut.
Whereas it's wholly rational for any individual bank to take a much more cautious and conservative approach to lending, it's wholly irrational for all of them to do so at precisely the same time
Lloyds TSB, HBOS and Royal Bank of Scotland, which owns NatWest, have taken government cash to strengthen their finances.
Mr Cameron added that other lenders should also cut rates.
The problem, lenders say, is that the key to mortgage costs is not the Bank of England's base rate but Libor - the London Interbank Offered Rate - which is the rate at which banks lend to each other.
The three-month sterling Libor rate - which has the greatest influence on new tracker mortgages - fell from 5.56% to 4.49% on Friday, its lowest level since the end of 2005.
But the rate remains almost one and a half percentage points above the Bank of England's base rate - still well above pre-credit crunch levels.
Nationwide
A number of building societies have said they could take weeks to decide whether to pass on the cut. This would be to consider the effect on savers and to monitor Libor.
The Nationwide, explaining its decision, said its borrowers would be "substantially better off".
"This is the right and fair course of action for Nationwide to take for all our borrowers at what is a very challenging time for everyone in the UK," said the society's chief executive Graham Beale.
Any changes to savers' rates will be announced later.
HOW MORTGAGE LENDERS RESPONDED
Lender
SVR before BoE decision
SVR after BoE decision
Rate change (percentage points)
HBOS
6.50%
Under review
�
Nationwide BS
6.19%
4.69%
-1.5
Abbey
6.94%
5.44%
-1.5
Lloyds TSB/ C&G
6.50%
5.00%
-1.5
Northern Rock
7.34%
Under review
�
Barclays
6.64%
Under review
�
RBS
6.69%
5.19%
-1.5
HSBC
6.25%
Under review
�
Alliance & Leicester
6.94%
Under review
�
Bradford & Bingley
7.09%
Under review
�
Bristol & West
6.59%
Under review
�
Britannia BS
6.30%
Under review
Yorkshire BS
6.60%
Under review
�
GE Money
10.39%
Under review
�
Coventry BS
6.84%
Under review
�
Standard Life
6.59%
Under review
�
Clydesdale & Yorkshire
6.64%
Under review
�
Chelsea BS
7.24%
Under review
�
Skipton
6.45%
Under review
�
SVR: Standard Variable RateAny changes take effect from 1 December
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