On a seasonally-adjusted basis, there were 29,510 housing starts.
In the year to June, construction work started on 110,530 new homes, a 7% increase on the previous year.
But the number of new homes being built is still far smaller than before the recession in 2008.
At that time, more than 180,000 homes were built in England.
The latest figures, from the Department for Communities and Local Government, reflect different rates of house-building in different parts of the country.
Housing starts have been strong in areas that include the M5 corridor between Devon and Worcestershire, north of the London green belt, Leicestershire, south Lincolnshire and Cumbria.
Starts have been "generally low" in areas that include a band running from Birmingham up to Manchester and spreading to North Yorkshire.
Eastern parts of Kent and Norfolk have also seen less house-building.
House construction is expected to rise further in the months ahead, following the launch of the government's Help to Buy scheme.
Earlier this week, it was announced that 10,000 people had applied for new homes under the scheme since it began in April.
It enables home-buyers in England and Wales to afford a house or flat, with the help of an equity loan from the government.
Buyers in Scotland have access to a similar scheme.
Source - bbc.co.uk - © 2013 BBC
