In the public sector housebuilding fell by 4% and private sector registrations fell by 1%.
In total 36,219 new homes were registered in Q3 compared to 36,955 a year ago.
Charles Haresnape, managing director, mortgages, Aldermore Group, said: “The drop in public sector registrations is a clear cause for concern. Creating supply continues to be the biggest challenge for both the private and social housing sector, so any slowdown is a worry.
“Affordability remains a challenge for many hoping to buy or are currently renting, but it’s crucial we have a consistent supply of housing coming through as well.”
Right to Buy has come under attack in recent weeks, as last week Shelter’s head of policy Toby Lloyd said the policy will worsen the housing crisis for first-time buyers by diminishing the UK’s limited supply of homes.
He also questioned the government's one-for one replacement pledge, which he reckoned will see homes sold in London and cheaper ones bought in other areas of the UK.
Before the election Prime Minister David Cameron said: “When a generation of hard-working men and women in their 20s and 30s are waking up each morning in their childhood bedrooms - that should be a wake-up call for us.”
Mike Quinton, chief executive said: "Despite the marginal drop in housing registrations this quarter, 2015 is still promising to be a strong year for new housing growth in the UK. Our year-to-date figures show that registrations in both the private and public sector are ahead of last year.
"The industry remains upbeat and is working hard to build the number of homes our country so desperately needs, despite the pressures associated with rapid growth."
