The Land Registry has reported an annual price increase of 5.3% for September.
This takes the average property value in England and Wales to £186,553.
Monthly house prices were up 1.0% since August 2015.
John Eastgate, sales and marketing director of OneSavings Bank, said: “House prices are bouncing back from what seemed like a moderating market, with annual price inflation reaching a six month high in September.
“Year on year price increases had slowed over the summer, so these numbers reverse that trend and as long as the scales remain heavily tipped toward demand over supply, continued growth is fairly certain in the long term. Little respite then for first time buyers, who struggle with the need to match higher house prices with larger deposits.
“Strong mortgage lending figures have so far been supported by year on year growth in remortgage activity, so this acceleration in house price inflation may yet further impact on the purchase market.”
The region with the most significant annual price increase is London with a movement of 9.6%; the capital also experienced the greatest monthly rise with a movement of 1.8%.
The North East saw the only annual price decrease with a movement of -0.3%. The region also saw the most significant monthly price decrease with a fall of 0.3%.
Meanwhile, the number of completed house sales in England & Wales decreased by 4% to 81,696 compared with 84,691 in July 2014. The number of properties sold in England and Wales for over £1 million decreased by 9% to 1,413 from 1,555 a year earlier.
Repossessions in England and Wales fell by 50% to 471 compared with 943 in July 2014, while the region with the greatest fall in the number of repossession sales was London.