Australian voters are resoundingly sick of their bitterly polarised politics and a sizeable group says they would consider voting for a new centrist political party, according to the latest Guardian Essential poll.

The new survey of 1,830 voters found 71% agreement with the statement “I wish both sides of politics would try to meet each other in the middle more often” and 45% said they would consider voting for a new party that took ideas from both sides of politics.

A total of 45% of the sample agreed with the statement, “Political parties in Australia are too ideological.”

The latest weekly opinion survey has Labor continuing with a commanding lead over the Coalition on the two-party preferred measure, 54% to 46% – which is the same result as last week.

With marriage equality once again creating tension within government ranks, this week’s poll finds 61% support for the legalisation of same-sex marriage,and 26% opposition.

Women are more likely than men to support marriage equality and young people are considerably more supportive of the concept than voters over 65.

According to the survey, 81% of 18 to 24-year-olds support same-sex marriage, compared with 46% of over 65-year-olds.

While the Liberal senator Dean Smith has signalled he will press ahead once parliament resumes with a private member’s bill legalising same-sex marriage – a development that will trigger a discussion within the Liberal party about whether to move away from a plebiscite policy to a conscience vote position – the survey indicates voters are divided about how they would like the issue resolved.

Of the respondents, 50% said they wanted a national vote that would be binding on parliament, 23% favoured a vote in parliament without a preceding national vote and only 9% want a national vote followed by a conscience vote in parliament.

The voters most likely to favour a parliamentary vote, minus a plebiscite, were Greens voters (39%), voters aged over 65 (32%), university educated voters (29%) and people who support same-sex marriage (29%).

With disillusioned voters breaking away from the major parties in increasing numbers, the Guardian Essential survey asked a number of questions seeking to ascertain whether Australian voters would be attracted to a new centrist political party.

Thirty-seven per cent of the sample thought there was no substantial difference between the policies of the Liberal party and the Labor party – which perhaps explains the high level of frustration (71%) with the current levels of polarisation in the Australian political discussion.

Half the sample indicated it was not tribal, agreeing with the statement: “I don’t personally identify with either left-wing or right-wing politics.”

There was one contradictory answer in the sequence of six questions. While 45% expressed interest in a new centrist party, a further 43% said Australia didn’t need any more new political parties.

Voters were also asked whether they had favourable impressions of several world leaders with different ideological persuasions.

Respondents were most likely to have a favourable view of Canadian prime minister Justin Trudeau (51%), German chancellor Angela Merkel (43%) and French president Emmanuel Macron (41%) – two politicians from the centre-left and one from the centre-right.

Further down the pecking order was the British prime minister, Theresa May, on 33% support.

The Russian president, Vladimir Putin, had an identical favourability rating to the US president, Donald Trump – 16% – and the North Korean chairman, Kim Jong-un, got the thumbs up from 6% of the sample.

Coalition voters were more likely than average to have a favourable view of Theresa May (46%) and Donald Trump (23%).

Labor voters did not differ much from the average – except for their low rating of Trump (9% favourable).