House prices rose 3.4% in the three months to the end of November, the sharpest increase since late 2006, and are 8.2% higher than a year earlier, according to the monthly figures from the lender, part of Lloyds Banking Group.
"The performance of the market continues to be underpinned by a shortage of available properties, a strong labour market and keen competition amongst mortgage providers keeping rates close to historic lows," Russell Galley, managing director of Halifax, said.
The Bank of England plans to start raising interest rates in the coming months from their record low 0.1%, although the emergence of the Omicron variant of coronavirus means markets are split over whether this will happen at next week's policy meeting.
Halifax said house prices rose 1.0% in November alone, the same increase as in October.
British house prices have risen strongly through most of the COVID-19 pandemic, in line with many other big economies, reflecting an increased demand for space to work from home and - in Britain's case - temporary tax incentives to move house.
The most recent official data showed house prices in September, the last month when the tax break applied, were 11.8% higher than a year before, just off a 15-year peak of 12.6% in June when the tax incentive started to be phased out in England.
But Halifax said there were signs that the shift in demand towards larger, less central housing was reversing, as prices for apartments rose faster than those for detached houses.
"We would not expect the current level of house price growth to be sustained next year given that house price to income ratios are already historically high, and household budgets are only likely to come under greater pressure in the coming months," Galley said.
(Reporting by David Milliken; editing by James Davey and Kate Holton)