HSBC is writing to 30,000 of its tracker and variable-rate mortgage customers to put the case for overpaying on their home loan.
The bank said it was taking the unusual step in response to the recent dramatic cuts in UK rates.
"Tracker customers have seen their rates fall 3.5 per cent in just four months. It is absolutely in their favour to make use of today's historically low interest rates," said Martijn van der Heijden, HSBC's head of mortgages. "Overpaying their mortgage could reduce its term by years and save them thousands of pounds in interest."
The bank reckons that a monthly overpayment of just £100 on a loan of £150,000 will cut more than four years off the term of a 25-year repayment mortgage and save nearly £12,000 interest.
Mr van der Heijden also believes borrowers should not get too used to the low cost of borrowing.
"There is a genuine danger for homeowners in allowing their lifestyles to become accustomed to the current low rates," he explained. "Interest rates will increase at some point and it will feel painful for those borrowers who have soaked up the benefit of lower mortgage payments by extending their spending habits."