The Greens say they will “wave through” Labor’s housing bill after holding out for months, handing the government a victory on key pieces of its housing agenda.

The Greens capitulated late on Monday after a lengthy deadlock over the Albanese government’s Help to Buy and Build to Rent package.

The legislation will go to a vote on Tuesday, and is expected to pass the Senate without the support of the Coalition.

The Help to Buy scheme promises a contribution of up to 40 per cent for 40,000 low and middle-income families to buy a home of their own.

The Rent to Build bill will provide tax concessions to encourage more rental construction.

The Greens dugs in their heels for months in the hope Labor would do more to support renters and improve housing affordability, calling for changes to property investor tax concessions and caps on rent rises.

While unable to extract rent caps or other major concessions, the Green were able to secure an extra $3 billion of investment for social housing in negotiations for the Housing Australia Future Fund.

Greens leader Adam Bandt confirmed his party’s support for both bills on Monday but said the government had missed a “golden opportunity” to tackle the big drivers of the housing crisis.

“The issue needs to be fixed,” Bandt said in Canberra.

“Otherwise whole generations are never going to be able to own their own home, and renters are going to be pushed to breaking point.”

Bandt said his party had pushed as hard as possible for caps on rent increases and phase out tax concessions for property investors.

“There comes a point where you’ve pushed as far as you can,”  Bandt said.

Greens housing spokesperson Max Chandler-Mather said the party had wanted to get Labor to “do something more than tinker around the edges of this devastating housing crisis”.

He said the Greens had “pushed as hard as we possibly could”.

Housing Minister Clare O’Neil would not speak for other Senate crossbenchers but said the changes “have now got a really clear passage through the parliament”.

“I’m glad [the Greens] have finally seen the light,” she said on Monday.

“But it doesn’t excuse the fact that they have played politics on housing for 2½ years, and the net effect of the Greens in this term of parliament is to delay action on housing.”

Push for easier home loans

Meanwhile, opposition housing spokesman Michael Sukkar will blame banking regulations for making it harder for first-home buyers to secure loans.

Sukkar will hint at “a comprehensive package” of reforms aimed at freeing up access to finance during remarks to the National Press Club on Tuesday.

The Coalition wants to weaken “responsible lending” obligations imposed on banks after the global financial crisis that it believes are too cumbersome and create barriers for first-time buyers.

“If there’s one message I want Australians to take away from my remarks today, it’s that the Coalition will not accept a generation of Australians not having the same opportunities that previous generations have enjoyed for home ownership,” Sukkar will say.

He will go toe-to-toe with Chandler-Mather on Tuesday at the NPC debate after the minor party committed to backing Labor’s shared equity scheme and build-to-rent bills.

Both housing bills failed to attract opposition support, leaving the government to negotiate with the Greens and independent Senate crossbenchers.

-with AAP