Falling house prices are another reason to overpay your mortgage
Lloyds TSB has reported more than 27,000 requests from customers to overpay their mortgage since November's sharp interest rate cut.
Lloyds, which owns the Cheltenham & Gloucester brand, said it followed customers on tracker mortgages seeing their payments shrink.
Other lenders contacted by the BBC said they did not collate such figures.
But the Council of Mortgage Lenders said it encouraged overpaying mortgages for those who could afford it.
"Now is also a good opportunity for borrowers on interest only mortgages to switch to repayment mortgages to use this period of low interest rates to start to pay down their loans," said CML director general Michael Coogan.
Overpaying is when people pay off more of their home loan than is required each month - reducing the amount they owe on a property.
Many financial advisers have been advising homeowners to use the tactic to take advantage of low rates because, as house prices have decreased, the level of equity a customer holds in their property is also likely to have fallen.
By making mortgage overpayments, borrowers may help maintain or even increase the equity on their property.
They can also potentially reduce the term of the mortgage - and because the capital is paid off more quickly, the total interest bill is reduced.
Rates passed on
The Bank of England base rate is currently 1.5%, having fallen from 5% since September last year, including a fall from 4.5% to 3% in November.
Lenders have passed on at least some of the fall to mortgage holders on tracker or variable rates.
Lloyds TSB said a homeowner with a £150,000 mortgage who was on a tracker deal or standard variable rate would have seen their monthly repayments fall by about £380 a month since interest rates first began to fall in December 2007.
Nationwide said it had no figures on repayment enquiries, as customers could overpay up to £500 a month on top of their scheduled repayment without seeking permission.
Halifax said that its borrowers could pay an extra 10% of the amount due on a mortgage in any 12 month period.