House prices will rise by up to 8% next year to build on strong gains this year, according to a forecast from Halifax.
It said further economic recovery and continued low interest rates would support a broadly similar increase to this year, which has already seen prices go up 7% in the first 11 months.
But a price surge in London, which has seen the steepest rises, is expected to slow down, the bank added.
The forecast comes in the wake of a warning from Business Secretary Vince Cable that the Government might need to review its flagship Help to Buy programme amid what he called a "raging housing boom" in the capital and the South East.
Halifax's prediction of a house price rise of 4%-8% for the next 12 months follows a similar outlook from Rightmove, which expects a 6%-8% increase.
But the bank believes that after next year there will only be a muted rise, as increased house building eases demand and earnings growth remains subdued, while an eventual rise in interest rates nears.
Halifax's housing economist Martin Ellis said the market had been stronger than expected this year.
"Low interest rates and higher consumer confidence due to increasing evidence that a sustainable economic recovery may now be under way are helping to stimulate housing demand," he said.
Schemes such as Help to Buy - which helps those struggling to put together a deposit - and the recently terminated Funding for Lending scheme (FLS) - incentivising banks and building societies to lend - have also boosted demand.
Activity has picked up with transactions likely to exceed a million for the first time since 2007, Mr Ellis added.
"Mounting signs that the economic recovery is becoming firmly established, together with a predicted decline in unemployment, should further boost consumer confidence.
"This will increase the likelihood that more people will consider buying a property in 2014, therefore supporting housing demand."
The rise will be contained by the slow pace of pay growth, the end of FLS, and an increase in supply from homeowners willing to put properties on the market now prices have risen, will all act as a constraint, he added.
Mr Ellis said there was "little sign of the excessive behaviour associated with a house price bubble" for now, saying prices remained 12% below their August 2007 level.
Price rises have not been accelerating but have been steady at a quarterly rate of 2%. In contrast, each year between 2001 and 2004 saw double digit increases, he said.
Only in London were present prices become significantly higher relative to incomes compared with long-term averages.
"We expect this factor to act as a constraint on house prices in the capital, leading to a slowdown next year," Mr Ellis said.
He added that the improvement led by the capital this year was expected to become more broadly based across the country over the next year.
The figures come after remarks by Mr Cable to the BBC that the boom in house prices in the capital threatened a future where "the only people who can live in large parts of London are foreigners and bankers".
Policymakers at the Bank of England have been making clear for the last few months that they are prepared to intervene should an unsustainable house price bubble become likely.