Equality advocates are hoping a High Court legal challenge will kill off the federal government’s postal survey on same-sex marriage but, at the same time, they’re buoyed by an opinion poll in former prime minister Tony Abbott’s electorate of Warringah.

A push to stop the controversial plebiscite will be heard in the High Court in early September just days before the vote is scheduled to begin.

Chief Justice Susan Kiefel on Friday said the full bench would hear the case on September 5 and 6.

The court received two separate applications. One came from the Public Interest Advocacy Centre on behalf of Tasmanian independent MP Andrew Wilkie, advocate Felicity Marlowe and Parents and Friends of Lesbians and Gays.

Another was lodged by the Human Rights Law Centre on behalf of Australian Marriage Equality and Greens Senator Janet Rice.

Gay rights campaigners question the legal validity of the postal plebiscite and its $122 million cost.

They’re also concerned campaigning in the lead-up to the vote could tip over into hate speech and discrimination.

Still, they’ve been encouraged by an Australia Institute poll which suggests Mr Abbott’s own electorate overwhelmingly supports gay marriage.

The former prime minister, who opposes same-sex marriage, this week linked the plebiscite to religious freedom, freedom of speech and political correctness when urging people to “vote No”.

But in his Sydney electorate, 70 per cent off 700 resident surveyed said same-sex couples should be able to get married.

Liberal voters polled 60.3 per cent in favour, Labor voters 88 per cent and every Green polled expressed support.

“There is a massive mood for change on marriage equality around Australia and this poll is further evidence of that,” Australia Institute executive director Ben Oquist said in a statement on Saturday.

“Warringah voters look set to overwhelmingly back marriage equality and they do not appear to be buying into the line that the survey has anything to do with free speech or political correctness.”