The Halifax said that prices were up by 0.3% in September which marks the eighth consecutive month of growth.
On a annual basis prices were up by 6.2% which marked the highest annual rise since June 2010. As such the average price of a house in the UK now stands at £170,733.
Nicholas Ayre, managing director of homebuying agency Home Fusion, said: “The housing market continues to gather momentum after years in the doldrums.
“This will inevitably fuel talk of a house-price bubble, even though the recent strong increase in private housebuilding on the back of the first phase of the Help to Buy scheme is encouraging.
“However, will flats and houses be built fast enough to dampen rising demand and will some of the new developments in London particularly be at a price point suitable for first-time buyers?”
Halifax's housing economist, Martin Ellis, also expressed concerns about the lack of supply.
He said: "Housing demand has risen more quickly than supply in recent months, putting upward pressure on prices.
“There are signs that supply is beginning to respond to the pick-up in demand, which if continued should help to constrain the upward pressure on prices.
“The recent strengthening in house prices is increasing the amount of equity that many homeowners have in their home, enabling more to put their property on the market for sale. Levels of housebuilding are also increasing, albeit from a very low base"
