The Albanese government says 13,700 affordable homes have been approved for construction under the policies it has so far managed to legislate, as it prepares to do battle with the Senate this week over two more housing initiatives that are being blocked by the Coalition and the Greens.

With only the Senate sitting this week, the government will attempt to ease a logjam of legislation that includes its help-to-buy and build-to-rent housing schemes, as well as its structural reforms to the Reserve Bank of Australia and the establishment of an environment protection authority.