Support in Australia for same-sex marriage and for a conscience vote in the Coalition are at an all-time high, according to a new poll.

The poll commissioned by Australian Marriage Equality found that 72 per cent of Australians support same-sex marriage being legalised, according to a Fairfax report.

• High Court case on same-sex marriage laws to begin today
• Senator flags gay marriage bill

Seventy-seven per cent of Australians also think that Coalition politicians should be granted a conscience vote on same-sex marriage.

A poll commissioned by Australian Marriage Equality has found 72 per cent of Aussies want same-sex marriage legalised #sun7

— Sunrise (@sunriseon7) July 14, 2014

Australia’s parliament is largely out of step with the general population on the issue of marriage equality. #qanda

— Natalie Hudson (@natalie_mae1) July 14, 2014

The poll comes a day after Liberal Democratic Senator David Leyonhjelm challenged Tony Abbott to allow his MPs to vote freely on same-sex marriage.

Mr Leyonhjelm said that he would move a private member’s bill to amend the federal marriage act as soon as that happened.

Support for #marriageequality is now higher in Australia than New Zealand or the UK when it was passed http://t.co/pF71miQb1X #auspol

— Broede Carmody (@BroedeCarmody) July 14, 2014

The latest poll shows that support for marriage equality is increasing amongst Australians, up from 65 per cent last August.

“With Australians across all key demographics supporting marriage equality in record numbers, it’s fair to say the public has made up its mind, the community debate has been won, and it’s time for politicians to act,” Australian Marriage Equality national director Rodney Croome told Fairfax.