Associations will be able to apply for funding as far ahead as 2028/29 under the new scheme.
May also announced that, to date, almost £600m has been provided to eight housing associations to build just under 15,000 new affordable homes.
The prime minister urged housing associations to lead the way in transforming how housing is delivered in the UK.
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Speaking at the National Housing Summit, May said: “Last year, I told the big commercial developers that we would give them the support they asked for – but that, in return, we expected them to do their duty by getting homes built.
“Today, I’m asking housing associations to use the tools we have given you.
“Not just to build more homes, though, of course, more homes are needed.
“But to take the lead in transforming the very way in which we think about and deliver housing in this country.
“Rather than simply acquiring a proportion of the properties commercial developers build, I want to see housing associations taking on and leading major developments themselves.”