Prime Minister Julia Gillard has conceded the Australian Labor Party’s Left faction has the numbers to drive an historic change to the ALP’s platform on same-sex marriage and is seeking a deal to allow MPs a conscience vote on the floor of parliament.

Ms Gillard on Friday afternoon met with the party’s powerful factional bosses in Sydney to discuss a way forward on the issue of gay marriage which is causing divisions within the Right faction, leaking support to the Left, party sources said.