UK Asset Resolution (UKAR), which is winding down the loans of 467,000 customers, said it repaid £6.2 billion to the government in the 15 months to the end of March, 50 per cent more than the total over the previous two years, taking the aggregate repayment to £10.4bn of the £48.7bn it owed when set up in October 2010.
It said: "House prices have increased faster than expected over the past 15 months, which, combined with continued low rates of interest, is good news for our customers and has driven increased redemption activity.
"However, despite the more positive conditions, many households continue to be under financial pressure."
Richard Banks, chief executive, said that while 93 per cent of borrowers were on track with their repayments, and the proportion in arrears of more than three months (including repossessions) fell by 39 per cent last year to 15,500, that total could jump back to 37,000 if rates were to go up.
But he added that rises which were "small and often over a long period would be better than sudden, very large increases".
Economists have begun to speculate that interest rates may rise early next year. Mr Banks said UKAR had reduced arrears by working with customers in financial difficulty.
UKAR was reporting an underlying pre-tax profit of £1.26 billion in the 15-month period, up by £186 million on the previous 12 months.
Balance sheet assets have reduced from £115.8bn in October 2010 to £74.9bn. The business said it is contacting customers who may be at more risk when interest rates begin to rise, including 31,000 with interest-only mortgages and those who will be repaying their mortgage in retirement.
Mr Banks said UKAR had received further approaches from potential buyers for the better-performing parts of its mortgage book, and he expected to do deals over the next few months, enabling a faster repayment of the government debt.
"We are always looking for opportunities to sell parts of the book. There are good opportunities to sell good-performing assets at full price," Mr Banks said.
UKAR last year sold a portfolio of former Northern Rock loans to US private equity firm J.C. Flowers and debt recovery business Marlin Financial for a combined £400million.
Mr Banks said he was confident taxpayers would get back all the money spent on the rescue of Northern Rock and Bradford & Bingley four years ago, with the "vast majority" of the funds repaid by 2020. UKAR has set aside £116 million to deal with past misconduct by Northern Rock and Bradford & Bingley, including compensation for mis-sold payment protection insurance.