The most pro-European member of Theresa May’s cabinet has appealed to Remain voters to abandon hope that Brexit can be reversed – and instead back the prime minister to secure a “special partnership” with the EU.

The appeal to those who voted to stay in the EU, including Labour, Liberal Democrat and Scottish National party supporters – by work and pensions secretary Damian Green – is the Tories’ latest attempt to widen their appeal for the 8 June general election.

Green, the closest ally and oldest friend of the prime minister in the cabinet, says in an interview with the Observer that it is time for Remain supporters, whose cause he championed during the referendum campaign, to stop playing games and deluding themselves that the UK can stay in the EU.

Instead, he says, they must recognise that the country faces a “huge historic task” and one of the “most momentous half decades” in its history as it tries to replace full EU membership with a workable alternative.

Tory strategists know that if they can win over a large number of non-Tory Remain supporters, as well as those hardline Leave voters deserting Ukip, then May could secure a huge “national mandate” that would bolster her hand in Brexit talks due to start next month.

“There are two things you can do as a Remainer, as I was,” Green says. “You can either say we argued the case and we lost, so now we have to think about what is best for the country, or you can continue trying to play games to say it didn’t really happen, and can we reverse it.

Play Video 0:51 PM: There is no Mayism, only good, solid Conservatism – video

“It seems overwhelmingly more sensible and more in the interests of this country to ensure the government gets the best deal here – to get a close and special partnership with the EU.”

He adds: “Given this huge historic task, you have got a pretty stark choice of leaders – Theresa May or Jeremy Corbyn – and that is what we are pointing out to the country.”

As the Lib Dems, whose campaign centres on a call for a second referendum, struggle to make progress in the polls, and Labour lags behind the Conservatives, the Tories are stressing the potentially disastrous consequences of failure in the Brexit talks. Launching the Tory manifesto on Thursday, May said a bad deal would be “dire” for working people in the UK.

In an apparent rebuke to rightwing Conservatives who say the UK should be prepared to leave the EU with “no deal” rather than accept compromises over issues such as the divorce bill, Green says it is essential that an agreement is reached, and insists that this will require give and take. “No negotiation has ever succeeded without an element of compromise and similarly no compromise ever satisfies everyone 100%,” he says. “I am sure that all sensible people recognise that first of all there is a deal to be done that is mutually beneficial. That is the first thing you need.”

He refuses to draw comparisons with Margaret Thatcher’s ideology, but says the current prime minister is every bit as tough. “Mrs Thatcher saw dragons that needed to be slain in the 70s and was a tough-minded woman who succeeded. Theresa in 2017 is a tough-minded woman who succeeds – but there are different dragons to be slain.”

Facebook Twitter Pinterest ‘Dragons Theresa May wants to slay are different to those Margaret Thatcher targeted as prime minister’ Photograph: PA

He adds: “Theresa is a very tough individual. She is a tough individual who when convinced that the path is right will pursue it.”

In last June’s EU referendum, 39% of Tories, 65% of Labour supporters and 68% of Lib Dems backed Remain. But recent analysis by YouGov suggests many Remainers now accept Brexit must happen. YouGov said there were now three identifiable groups: the “hard leavers” who make up 45% of voters; the “hard remainers” who still want to try to stop Brexit (22%); and a group of pragmatic leavers, 23% of the electorate, who voted Remain but believe the government has a duty now to deliver on the referendum vote.

The Tory advantage has plummeted since the party’s manifesto launch, according to a series of polls for Sunday newspapers. YouGov for the Sunday Times has the Tories’ lead down to nine points – the first time it has been in single figures in a mainstream poll since May called the snap election on 18 April.

An Opinium/Observer poll – conducted before the Tory manifesto launch – shows 47% of voters most trust the Tories to handle the Brexit process, against 13% who say Labour would do the best job. Conducted after the launch of Labour’s manifesto on Tuesday, but before the Tories’ on Thursday, it puts the Tories on 46% (down a point on a week ago), Labour on 33% (up one point), the Lib Dems on 8% and Ukip on 5% (both unchanged).