Reuters
The 32,110 affordable homes built in the period was less than half the 66,600 built the previous year, and the lowest number since 1991/92.
The number of homes built for social renting - properties rented out by the council to those most in need - fell to just 6,550. That figure is 80% lower than the last year Labour was in power, in 2009/10, when the figure was 33,490.
Labour housing spokesman John Healey said in an emailed statement that the provisional figures released by the Department for Communities and Local Government (DCLG) were "disastrous."
He said: "They show we are now building the lowest number of social rented homes since records began. And the number of affordable homes to buy has fallen by two-thirds since 2010."
Healey also echoed concerns that the government had tried to cover up poor housebuilding figures simply by changing its definition of "affordable homes" when it launched its new "Affordable Homes Programme" in January.
The government widened the term's definition to include "starter" properties on sale for up to £450,000 - despite that being over 16 times the average UK salary of £28,000. Healey said it was an "insult to the public's intelligence" that "the government tried to hide their failure to build more homes by branding more homes as 'affordable.'"
Even with the new definition, the number of homes constructed for "affordable" home ownership dropped from 15,970 last year to 3,430.
The drop was similarly dramatic for "affordable" homes for private rental, the number of which fell from 40,730 in 2014/15 to 16,550 in 2015/16.
He said: "Delivery is normally lower in the first year of any new housing programme and so these figures are expected as part of a 5-year house building cycle.
"Building more homes is an absolute priority for this Government, which is why we have doubled the housing budget to £8 billion and we now have the largest affordable housing programme in 40 years," he said.
"Furthermore, latest figures out this week show overall house building is at its highest level in eight years and we will be publishing our White Paper shortly, setting out our plans to build more homes and more quickly," he added.