Jeremy Corbyn is clearly up for the fight but the polls show he and his party have a mountain to climb

Punchy, combative, fired up. Jeremy Corbyn’s first speech as Labour hit the campaign trail on Thursday was a taste of how the party hopes to turn its status as the underdog in June’s general election to its political advantage.

Corbyn does not relish the mannered conflicts that take place across the dispatch box in the House of Commons; but he is happiest at packed rallies of enthusiastic supporters, or out meeting members of the public.

Play Video 1:45 Journalist booed after asking Corbyn about 'Islington elite' – video

His team hope they can turn his authenticity to good use, and capitalise on Labour’s status as the political underdog, written off by Westminster – and much of the media.

Labour viewed last year’s Brexit vote as a kick up the backside for the political establishment, and a cry for help from voters who feel abandoned by politicians; and the party hopes Corbyn’s message of smashing “cosy cartels” will appeal to those people.

There are several pitfalls with this approach. One is about detailed policy. Corbyn’s close allies, including his director of communications and strategy, Seumas Milne, have long been convinced that a spring election was a possibility, and the shadow cabinet announced a flurry of policies over the Easter break, including free school meals and a £10-an-hour minimum wage by 2020.

But headline-grabbing announcements are one thing, and a costed, worked-out manifesto is another. One senior adviser told the Guardian policies in some areas were hastily being “drawn up on the back of an envelope”.

General election manifestos are subject to the sometimes brutal scrutiny not just of the rightwing press, but of independent thinktanks, such as the Institute of Fiscal Studies, which will calculate whether they think the sums add up.

And, whether it is fair or not, Labour is particularly vulnerable to the charge – repeated weekly at prime minister’s questions by Theresa May – that it would “bankrupt Britain”, by throwing money at every problem in society.

The ferocity of the onslaught on the shadow chancellor, John McDonnell, when he said those earning £70,000 were “rich” and should pay more tax, were just a taster of they way this argument could play out. Veterans of the 1992 campaign, when Neil Kinnock failed to boot the Tories out of office, remember the power of the “Labour’s tax bomb” attacks.

A second pitfall with Corbyn’s populist playbook is that it may be too late for the party to get a hearing. If voters have already decided he is weak on security, or a lacklustre leader – or that Labour is too riven by internal conflict to govern the country, a message the Tories intend to hammer home – they may not be prepared to listen.

The third pitfall is Brexit. Labour constituencies include heavily leave-voting areas, which may be receptive to May’s argument that she’s called the general election so she can “get on with the job” of taking Britain out of the European Union. But it also hopes to hold on to liberal, strongly remain-voting areas, that may feel betrayed by Corbyn’s decision to whip his party to support triggering article 50, and open to Tim Farron’s ardently pro-remain Liberal Democrats.

Corbyn was introduced on Thursday by Dawn Butler, the Brent MP who was one of those who resigned from the shadow cabinet rather than accept the party whip and vote for article 50, underlining how the party is struggling to negotiate the issue.

Labour hopes to steer the debate in the coming weeks away from Brexit, and on to inequality, schools, hospitals, public services. But judging by the way May handled PMQs on Wednesday, strafing Labour backbenchers with disobliging past comments about their leader, they will have to fight hard to shift the agenda.

As the rambunctious leave campaigners showed last year, the political establishment sometimes get it badly wrong. But Corbyn and his close advisers, many of them veterans of decades-long battles on the left, are never happier than when they are the underdog; and sometimes with the latest polls showing Labour lagging up to 24% behind, they have a mountain to climb.