In the year to June, 131,060 homes were completed, a rise of 15% on the same period a year ago.
On a quarterly basis, between April and June, the number of completions rose by 22%, compared to 2014.
However, the number of homes being started fell by 1% over the year, to 136,320, and by 6% on a quarterly basis.
The increase in completions was welcomed by the National Housing Federation (NHF).
"Today's figures are encouraging as they show house building is at its highest level since 2008," said Henry Gregg, the NHF's assistant director of campaigns.
"However, we need to continue to increase our efforts as a nation to build the homes that are desperately needed. Last year alone we built less than half of the homes needed," he said.
The housing charity Shelter described the drop in housing starts as "shocking".
"Once again, these figures show that we're not building anywhere near the number of homes needed each year, leaving millions of ordinary hard-working people priced out," said Campbell Robb, Shelter's chief executive.
"And worryingly, despite claims by the government that progress is being made to solve our chronic housing shortage, the number of new homes started has actually decreased."
The housing minister, Brandon Lewis, welcomed the figures, but admitted there was more to do.
"That is why we have outlined plans to deliver 275,000 affordable homes by the end of this Parliament," he said.
Last week the Royal Institution of Chartered Surveyors (Rics) accused the government of failing to build enough homes.
It said that the number of homes for sale per surveyor in England and Wales was at a record low, and that the lack of supply would force prices up still further.
During the election campaign, David Cameron promised that 200,000 homes a year would be built by 2017, in addition to 200,000 starter homes by the end of the parliament.
The number of new homes being built in England has risen significantly over the last year, government figures show.