House prices rose by 6.1% in the year to September 2015, according to the Office for National Statistics (ONS).
That was up from 5.5% in August, and 5.2% in July. It brings the average house price to £286,000.
However, the rise is still much lower than a year previously, when prices were rising by more than 12%.
The Halifax has previously said that house prices rose by 8.6% over the same period, while Nationwide said the rise was just 3.8%.
Separately, the Land Registry for England and Wales announced that prices were up by 5.6% in the year to October.
The Land Registry includes cash sales, which typically represent about a third of the market.
The ONS figures show that prices rose fastest in Northern Ireland (10.2%) and the East of England (8.4%).
Regional House Prices
Region
Annual % change
Average house price
UK
6.1%
£286,000
England
6.4%
£299,000
Wales
1.1%
£175,000
Scotland
1.1%
£199,000
Northern Ireland
10.2%
£162,000
North East England
1.8%
£158,000
North West
4.2%
£184,000
Yorks and Humber
4.6%
£186,000
East Midlands
3.6%
£196,000
West Midlands
4.5%
£207,000
East
8.4%
£309,000
London
7.2%
£531,000
South East
7.4%
£359,000
South West
6%
£263,000
source: ONS
John Hawksworth, the chief economist at PwC, said house price inflation was now running at twice the rate of average earnings.
"The ongoing rise in house prices reinforces our projections that, by 2025, only around a quarter of 20-39 year olds in England may be owner occupiers, compared to around three quarters of over-55 year olds," he said.
Jeremy Leaf, a former chairman of Rics, said that, far from running out of steam, the housing market was re-energising itself.
"With the average property price in London now £531,000, unless you earn way above the national average salary, you have precious little hope of being in a position to buy," he said.
"Generation Rent is being left out in the cold: they have aspirations to buy but are being pushed further away from their goal."