Opposition to equal marriage has all-but-completely collapsed in Australia, a poll has found, with just a fifth of people still opposing same-sex marriage.

The lone Liberal Democrat Senator, David Leyonhjelm, who took office this month, announced last week that he would shortly introduce a bill to legalise same-sex marriage, hoping to win broad support from other parties.

According to the Sydney Morning Herald, a Crosby Textor poll commissioned by Australian Marriage Equality has found that 72% of Australians, support the introduction of same-sex marriage, with just 21% opposed, despite continued opposition within the government.

The poll found that a huge 85% of respondents with children support the introduction of marriage equality, while the majority of followers of every major religion also support the measure.

It also showed that 77% of Australians support allowing MPs to have a free vote on marriage equality, despite the government position.

The last vote on same-sex marriage in Australia was held in 2012, when the House of Representatives rejected it by a vote of 98-42, and the senate by 41-26.

It shows seismic changes from a 2011 poll, when 49% of people were in favour of same-sex marriage, and 40% opposed.

Australian Marriage Equality national director Rodney Croome said: “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.”

The governing Liberal party has long opposed equal marriage, with Prime Minister Tony Abbott giving his backing to the successful fight to end the brief recognition of same-sex marriage in the Australian Capital Territory last year.

However, there have been calls within his party for MPs to be allowed a free vote on the issue, with the Australian Liberal Students’ Federation passing a motion last week calling for the party to modernise.

Leyonhjelm called for cross-party cooperation in passing the bill earlier today, saying: “We are not asking for your approval. I ask merely for your tolerance.”