Surveys have suggested that a quarter of mortgage holders have been overpaying
Lloyds Banking Group is encouraging its borrowers to pay off their mortgages early.
Customers on variable rate deals can, for one year, overpay their mortgages by up to 20% of their loans.
Ultra-low interest rates mean UK households have saved about £20bn in interest repayments in the past year, the Bank of England has estimated.
Figures suggest that about one in four borrowers have used the money to accelerate their repayments.
Lloyds' current annual limit, common among lenders, is a 10% overpayment per year.
The Halifax, the main mortgage lending arm of the Lloyds group, was unable to say how many of its existing customers were using the current 10% facility, but a spokeswoman said it was responding to customer interest.
"We have had people phoning us up asking how much they can pay off," she said.
The advantage of overpaying is that it enables a borrower to pay off a loan more quickly, thus saving interest.
The one exception might be where the mortgage interest rate was so low that a borrower would be better off putting the extra payments into a savings account paying a higher rate of interest, after tax.
An analysis by the Council of Mortgage Lenders (CML) last year suggested that a quarter of the £20bn annual interest saving, brought about by the Bank of England's 0.5% bank rate, was showing up in higher mortgage capital repayments.
This analysis was backed up by a survey for Lloyds, suggesting that a quarter of mortgage holders were taking advantage of their much lower interest rates to pay off capital at a faster rate.
Stephen Noakes, commercial director of mortgages, Lloyds Banking Group said: "The average mortgage repayment has dropped by around £188 per month.
"And those on tracker mortgages have done even better - on average they are just over £400 a month better off."
It is normal for lenders to allow some overpayment on mortgage loans, each month or each year, before levying charges for the privilege.
Some allow up to £500 in overpayments each month; others stipulate a ceiling of 5% of the outstanding loan; and some allow 25% extra to be paid over the course of the particular deal, for instance during the two or three years of a fixed-rate mortgage.
Ray Boulger of mortgage brokers John Charcol, said: "Offset mortgages can allow you to overpay as much as you like, so long as you don't pay off the whole mortgage."
Despite the obvious attraction of making overpayments, January's edition of Trends in Lending, published by the Bank of England, found that they have not been common.
"The major UK lenders reported that overpayment of mortgages has not been widespread, partly because reduced payments had been used to finance spending and in some cases used to repay more expensive unsecured debts or held as precautionary saving," it said.