Labour will never defeat Nigel Farage if it continues to “sit on the fence” over Brexit and offers only “mealy-mouthed” support for a second referendum, the party’s deputy leader says today.

In an extraordinary intervention that exposes the tensions at the top of the party over Brexit strategy, Tom Watson warns that Labour will lose to Farage’s new “far right” Brexit party in May’s European elections if it continues to give the impression that “we half agree with him”.

Writing in today’s Observer, Jeremy Corbyn’s deputy argues that Labour needs to give much clearer and more enthusiastic backing to another referendum and also spell out a positive, radical vision of how a Labour government could advance socialist values by working with other centre-left parties inside the European Union.

Stressing that Farage is a real threat not just to the Conservatives but also to Labour, he writes: “We cannot just sit back, watch this fight on the far right, and allow Farage to prosper with a backward-looking brand of politics that offers no solutions. Instead we must offer a radical alternative based on our values that speaks directly to the people we represent and demonstrate Labour has a way forward out of the crisis.”

He adds: “Labour won’t defeat Farage by being mealy-mouthed and sounding as if we half agree with him. We won’t beat him unless we can inspire the millions crying out for a different direction. We won’t win if we sit on the fence about the most crucial issue facing our country for a generation.”

His comments – after opinion polls last week put the new Brexit party ahead of Labour and the Conservatives – reflects the frustration among senior Labour remainers about Corbyn’s lukewarm support for another referendum in which remain would be on the ballot paper.

They come as campaigners from both sides of the Brexit debate this weekend step up efforts to persuade millions of young people to register to vote in the 23 May elections so they have their say in the Europe debate.

The Vote for Your Future campaign, which attracted huge online interest as soon as it was launched last Thursday, is trying to reach about 3 million people aged 18 to 30 who are not registered before the deadline of 7 May.

The Electoral Commission says a third of the 9 million people in the UK in this age group are not currently registered to vote. This compares with just 4% of those over 65.

Callum Warriner, a young Brexit supporter and Dover councillor involved with the campaign, said: “It’s a national scandal that one in three young people aren’t registered to vote. With this year’s European elections being some of the most important ever, it’s critical that – no matter how they vote – young people are registered by 7 May.”

Student activist Amanda Chetwynd-Cowieson, who backs another referendum, added: “No matter how you vote in this year’s European elections – it’s critical that young people take part. On Thursday, within hours of launching, we were trending on Twitter and videos by our supporters had been watched by hundreds of thousands of people.”

Senior Labour party sources said arguments over whether Labour would commit to another referendum in its European election manifesto would break out in the parliamentary party as soon as MPs returned from their Easter break this week. Members of the party’s ruling national executive committee (NEC), dominated by Corbyn supporters, have been told that the NEC will approve the manifesto at a meeting on 30 April.

This will alarm remain-supporting shadow cabinet members who insist they should be fully involved.

While Corbyn is under pressure to back another public vote from the 80% of party members and many MPs who want the Brexit issue to be put back to the people, other Labour MPs say another public vote would damage faith in democracy.

A letter is circulating among Labour MPs who say that cross-party talks between the government and Labour on a possible soft-Brexit deal, which will resume this week, could collapse if Corbyn and his team insist that any agreement be conditional on a confirmatory referendum taking place.

Farage’s new Brexit party has swept into the lead in polling for the European elections. Photograph: Christopher Furlong/Getty Images

Stephen Kinnock, one of the authors of the letter, said: “It is vital that the public is left in no doubt about the fact that Labour is participating in the negotiations in good faith, and we believe that it would be a mistake if we were to start introducing our own red lines at the very moment that the prime minister appears to be softening hers.

“Let’s get a cross-party negotiated deal over the line first, and there will of course then be ample opportunity for colleagues who are campaigning for a second referendum to attach a confirmatory vote amendment to the withdrawal agreement implementation bill, should they wish to do so.”

Meanwhile, a survey of Tory party members by the ConservativeHome website found almost eight out of 10 now believe Theresa May should now resign, up from seven out of 10 a month ago.

Writing on the ConservativeHome website, the editor Paul Goodman says: “The second postponement of Brexit and the talks with Jeremy Corbyn are undoubtedly huge contributors to this lamentable rating. The latter especially is making campaigning uphill work indeed for many local government candidates. However, we suspect the biggest factor is the European parliamentary elections that are due to take place.”