The Nationwide building society said house prices are now rising at 6.5% a year, up from 5.8% a month ago.
It said the average price of a house or flat in the UK is £174,566, the highest since April 2008.
Separate figures from the Bank of England show mortgage approvals rose to the highest level since February 2008.
Despite recent price increases, the Nationwide noted that prices were still below the peak of the market, seen six years ago.
"Prices are still around 6% below the all-time high recorded in late 2007," said Robert Gardner, Nationwide's chief economist.
He said the improvement was the result of the better outlook in the jobs market, and "a brighter economic outlook, which has helped to bolster sentiment".
On a monthly basis, prices increased by 0.6%, slightly slower than in October, when prices rose by 1% in one month alone.
The Bank of England said there were 67,701 mortgage approvals in October, up from 66,891 in September.
Although that is the highest figure for over five years, it is well below pre-crisis levels, when there were typically more than 90,000 mortgages arranged every month.
Other recent housing market surveys have recorded price growth rates around half that of the Nationwide.
The Land Registry said this week that prices in England and Wales were rising by 3.4% year on year. Land Registry figures are based on actual sales, instead of mortgage approvals, which are used by Nationwide.
However, the Land Registry estimates include a significant time lag.
The Office for National Statistics (ONS) said its latest estimate for house price inflation was 3.8%.
Some economists believe the Bank of England's decision to stop Funding for Lending (FLS) for household mortgages could now put a brake on the housing market.
From January, FLS will only be used for business lending.
But others have said the change will make little difference.
"House prices... look set to see further strong increases over the coming months despite the Bank of England ending Funding for Lending support for mortgage lending," said Howard Archer, the chief UK economist with IHS Global Insight. He is sticking to his forecast that house prices will increase by 8% next year.
Robert Gardner, of the Nationwide, said the change to FLS was likely to have a "fairly modest impact".
"After all, FLS is only one of the reasons why mortgage rates are at historic lows," he told the BBC.
He cited the Bank of England's policy of quantitative easing as being instrumental in that, a process which will continue.
Under FLS, banks and building societies have been able to borrow money cheaply, if they lend it out to individuals and businesses.