The index showed that house prices rose by 1.6% month-on-month, and 3.3% on a quarterly basis.
House prices rose by 7.3% in the year to September 2020, according to the latest Halifax House Price Index.
The index also showed that house prices rose by 1.6% month-on-month and 3.3% on a quarterly basis, leaving the average property priced at £249,870.
In addition, mortgage applications have surged to 12-year high.
Russell Galley, managing director at Halifax, said: “The annual rate of change will naturally draw attention, with the increase of 7.3% the strongest since mid-2016.
“Context is important with the annual comparison, however, as September 2019 saw political uncertainty weigh on the market.
“Few would dispute that the performance of the housing market has been extremely strong since lockdown restrictions began to ease in May.
“Across the last three months, we have received more mortgage applications from both first time buyers and homemovers than anytime since 2008.
“It is highly unlikely that the housing market will continue to remain immune to the economic impact of the pandemic. The release of pent up demand and indeed the stamp duty holiday can only be temporary fillips and their impact will inevitably start to wane.
“As employment support measures are gradually scaled back beyond the end of October, the spectre of increased unemployment over the winter will come into sharper relief.
“Therefore while it may come later than initially anticipated, we continue to believe that significant downward pressure on house prices should be expected at some point in the months ahead as the realities of an economic recession are felt ever more keenly.”
Guy Harrington, chief executive of Glenhawk, added: “Another month, but the narrative has not changed.
“The question now is how much longer can the housing market defy the COVID-19 gloom?
“Growing consensus suggests we are in for a nasty shock, unless the doom-mongers have got it very wrong and the economy can ride out an unemployment-led economic slump.
"As history has shown us, when it comes to the UK housing market, all bets are off.”