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.
More top news
A group of disabled students have made their debut performance at a shopping centre in Kent
Hampshire's Ian Walker narrowly leads the Volvo Ocean Race after arriving in Auckland with the Abu Dhabi Ocean Racing team
Brighton wheel bosses hope to keep attraction for another 5 years, long after the i360 is up and running