The Environmental Secretary has dropped to third place as Foreign Secretary Jeremy Hunt overtook him, according to the survey. Both Tory politicians are supported by soft Brexit MPs and Government loyalists. But a poll by 326 Politics shows Mr Hunt inching ahead.
ITV Peston co-host Anushka Asthana presented the poll on the show last night.
She said: “Membership leans towards a harder Brexit laying down a real challenge for candidates like Gove, Hunt or Stewart to prove their Brexit credentials.”
The poll findings come after Mr Gove suggested he would seek another Brexit extension if he replaces Theresa May as Prime Minister.
Mr Gove, appearing at leadership election hustings, said further delaying the UK’s departure from the European Union might be necessary to achieve a better withdrawal deal.
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He said: “If we are making progress and are on the verge of a deal, and we’ve had a good EU Council in October and we’re 99 per cent of the way there on Halloween, are we seriously saying we wouldn’t take a bit more time to get the deal done?”
But Mr Gove also told the audience no deal should be left on the table.
He said: “No department will be more affected by no deal than Defra and I’ve done my best to mitigate the damage.
“No deal would be a challenge but it has to be on the table. It’s not the best option.”
As Jeremy Hunt scoops up support, Boris Johnson received the backing of three key heavyweights who previously supported Mr Gove.
Rishi Sunak, Robert Jenrick and Oliver Dowden said Mr Johnson is the only one who can save the Conservatives, The Times reported.
During separate Tory hustings, Mr Johnson vowed to deliver Brexit and avoid the “potential extinction” of the Conservatives.
His stark warning was echoed by fellow Brexiteer Andrea Leadsom, who said a delay to the UK’s exit from the European Union could “spell the end” for the party.