The Greens will wave through Labor’s delayed housing policies in the Senate, dropping their months-long opposition on Monday after failing to secure any new concessions from the government.

Bills for a shared equity ownership plan and changes to tax settings designed to spur Australia’s build-to-rent sector will go through parliament before the end of the week, as the minor party promised to focus on campaigning for renters and blocking Opposition Leader Peter Dutton at next year’s election.