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%).