A 6.2% annual rise in prices in September takes average house values to £170,733 and represents the biggest year-on-year increase since 2010, the lender said.
The latest increase follows a 5.4% annual rise in August, which like September's increase was the strongest rate since June 2010.
On a month-on-month basis, prices rose by 0.3%, equalling the increase in August and marking the eighth month of rises in a row.
Fears have been growing that some stronger than expected price rises this year could be leading to a bubble, with borrowers over-stretching themselves.
The Government has brought forward the launch of the new phase of its flagship Help to Buy scheme from January to next week, and concerns have been raised about the further upward pressure this will place on house prices as demand is stoked further.
The new scheme will stimulate the whole housing market by offering state-backed mortgages to people with deposits as low as 5% who want to buy a new-build or an existing home.
House prices are 5.4% higher than last summer, figures from the Halifax showed last week. The lender said prices rose 0.4% in August from July, the seventh consecutive monthly increase, resulting in an average figure of £170,231.
New Bank of England governor Mark Carney recently addressed concerns that Government stimulus measures risk stoking another property bubble.
He said the Bank is "acutely aware" of the potential threats and said action will be taken to clamp down on mortgage lending if needed. RICS said the increase in supply was not enough to keep pace with the "sheer weight of demand".
All regions of Britain saw greater numbers of homes come onto the market, with sharp rises in the south west and north east in particular. Surveyors expect prices to continue rising, with a balance of 45% predictingprice rises rather than falls over the next three months.
Help to Buy offers Government loans to allow people to buy new-build homes with a 5% deposit, while Funding for Lending is designed to ease borrowing conditions for households as well as small businesses
While these schemes have helped fuel demand, supply has been squeezed by relatively few new properties coming onto the market as people wait for the right moment to sell.
RICS global residential director Peter Bolton King said: "It's not surprising that more and more people are looking to sell their homes. The buyers are out there and prices are on the up so if you're looking to move it's a good time to do so."
But he added surveyors are warily watching house prices inflate amid fears they will become unaffordable
Surveyors with increasing new instructions rose to a balance of 26% in August, from 16% in July, a report by the Royal Institution of Chartered Surveyors (RICS) showed.
And surveyors seeing house prices rise rather than fall climbed to the highest level in almost seven years with a balance of 40%, as the market is fuelled by Government stimulus schemes such as Help to Buy and Funding for Lending.
VIDEO: A new survey by the Royal Institute of Chartered Surveyors is predicting that the average house price could rise by about two per cent this year. The average cost of a home in this region is just under £300,000. Malcolm Shaw reports.
Southend has seen the biggest rise in house prices among the country's major towns and cities over the past year.
According to the Halifax the average selling price in the seaside resort was 14.8% higher than the previous year, rising to £198,418 by the end of 2012, compared with an improvement of 2.1% on average across the whole of Essex.
Basingstoke in Hampshire experienced the second biggest rise in house prices with a 14.7% gain, while three more towns within commuting distance of London - Rochester, St Albans and Dartford - make up the top five.
House prices in the Meridian Region will rise by almost two thirds in the next decade - the steepest rise in the country. A new report from the National Housing Federation says they'll soar by sixty one per cent by 2022 - bringing the average house price from £285, 000 to over £458, 000.
The paper blames years of not building enough homes for the rise.
A new law that makes squatting illegal comes into force today.
The legislation has caused great controversy. Those protecting the rights of people whose properties have been occupied say the change from civil to criminal offence is long overdue. While charities working with homeless people are worried the new law will lead to more people living on the streets.
Fred interviews Duncan Shrubsole from the homelessness charity 'Crisis', about a controversial new law making it easier to evict squatters.Read the full story ›
London & the South East dominate the least affordable areas, with mortgage payments in Kensington & Chelsea typically standing at 76.6% of disposable earnings.
Overall, mortgage payments have nearly halved as a proportion of income over the past 5 years from a peak of 48% seen in the autumn of 2007.