It’s said that it takes a conservative to bring about radical social reform, and they don’t come much more conservative than Australia’s Tony Abbott, who has bowed to pressure to allow his MPs a free vote on same-sex marriage, clearing the way for a change in the law as early as August.

The unexpected move, signalled in parliament this week, reflects Mr Abbott’s acknowledgement that – despite his opposition to broadening the Marriage Act – the public and political momentum has become unstoppable.

No one is more pleased than the Prime Minister’s gay sister and fellow Liberal Party politician, Christine Forster. She said that she plans to marry her long-term partner, Virginia Edwards, and is confident that Mr Abbott will attend the wedding.

Ms Forster told ABC TV she expected to see same-sex marriage legalised this year and was delighted by the prospect of it happening under her brother’s leadership. “That will be for me one of the proudest moments of my life,” she said.

Last weekend’s Irish referendum reignited debate in Australia, and prompted the opposition Labor Party to announce the introduction of a private member’s bill.

However, like two others already before parliament, the bill was doomed to fail unless Mr Abbott, a devout Roman Catholic who once studied for the priesthood, allowed his Liberal politicians a conscience vote – something he has always resisted.

But on Wednesday, he abruptly changed his stance, declaring same-sex marriage an “important issue” that ought to be “owned by the parliament and not by any particular party”.

That was interpreted as sanctioning a multi-party approach, likely to translate into a private member’s bill co-sponsored by the Liberals and Labor. Mr Abbot said it was up to his MPs and senators to decide whether to have a free vote – a move they are almost certain to support.

Last time the issue was debated, in 2012, it was comprehensively defeated in both houses of parliament.

Since then, though, increasing numbers of politicians have publicly changed their minds. And with Labor already committed to allowing a free vote, the reform is likely to pass.