Sentiment for an Australian republic has fallen sharply in the wake of the tour by William Mountbatten-Windsor and Kate Middleton, new polling from Essential Research shows, and women are far more enamoured of remaining a monarchy than men.

For the first time since 2010, support for Australia becoming a republic is now below that for remaining a monarchy: just 33% of voters are in favour of becoming a republic, compared to 42% who are against it (25% had no opinion), a dramatic reversal from June last year, when support for a republic outgunned opposition 39%-35%.

And there’s a dramatic gender difference: just 24% of women favour a republic, while 42% of men back it. Unexpectedly, there is little difference between different age groups on the issue, while unsurprisingly Liberal voters are strongly opposed, 58%-22%.

On the question of whether voters think Australia will ever become a republic, 46% say it’s likely (down 6%) and 37% say unlikely. Again, men and women split significantly: 55% of men say it’s likely and only 38% of women say it’s likely. And 54% of voters approve of William Mountbatten-Windsor becoming King of Australia at some point in the future — which he will do when both the current monarch, Elizabeth Windsor, and her son Charles die. Forty-nine per cent of men approve of a putative “King William” and 60% of women, with older voters slightly more likely to approve.

Voters are opposed to the purchase of F-35 fighter aircraft 52%-30%, Essential found. The purchase of the controversial aircraft, which will cost $12 billion to purchase and another $12 billion to operate, was announced last week by the government. Liberal voters support the purchase 49%-33%, but Labor, Greens and other voters are all strongly opposed by factors of 3 to 1. Men (35%) are more likely to support the purchase than women (23% — unclear if they were piloted by a prince).

Opposition Leader Bill Shorten’s proposals to reduce the influence of unions in the Labor Party make 26% of voters more likely to vote Labor, Essential also found, while making 6% less likely. Fifty-nine per cent say they makes no difference. It’s hard to disentangle partisanship from that question, though, as 10% of Liberal voters said the reforms made it less likely they would vote Labor, an unlikely outcome except if understood as an expression of reflexive hostility to anything proposed by Bill Shorten no matter what the circumstances. More telling is that 71% of Liberal voters say the reforms will make no difference to their voting intention and only 15% say they will make them more likely to vote Labor.

On voting intention, Labor has benefited from a further decline in the Coalition’s primary vote. The Coalition has lost another point on its primary vote (40% — down more than 5 points from September), while Labor has picked one up (38%) and the Greens have lost one (10%). With the Palmer United Party remaining on 5%, that produces a two-party preferred outcome of 52-48 in the opposition’s favour.