It’s getting tenser by the interview in the campaign to keep the UK in the European Union. On Friday morning it was a tired-looking David Cameron who snapped at Good Morning Britain’s sofa-queen, Kate Garraway, when she pushed him on immigration.

Come the evening, it was Jeremy Corbyn’s turn to have a raw nerve exposed. Talking on the lawn outside Cardiff city hall, where Corbyn was due to speak on the Labour case for EU membership, the BBC’s Mark Mardell asked the MP for Islington North whether he was pulling his weight in the Remain campaign. What had happened to his Midas touch in mobilising the faithful? “What a strange question,” said Corbyn, screwing up his face, before listing the many events in his impressively packed schedule. “Watch me go tonight,” he told Mardell in so many words.

It was an ill-advised hostage to fortune. “It’s hard to make the EU sexy,” the event’s compere, Baroness (Eluned) Morgan was later to admit. Early speakers in the grand Edwardian assembly hall were not helped by a dodgy microphone, cutting out one moment only to come back to life the next to ear-piercing effect.

The shadow welfare secretary, Owen Smith, stirred the placid, and elderly, audience as much as anyone by mentioning a nearby memorial to the “fallen heroes of the International Brigade”. “There is a wonderful inscription,” he said. “None shall be free, until all are free ... Get out there and fight for it.” But that’s not something you can necessarily sell on the council estates of Merthyr Tydfil, Morgan was again to admit.

The Remain case undoubtedly needs to find some pizzazz from somewhere. The task of enthusing Labour voters and motivating them to register and then actually vote is increasingly urgent. Labour voters could hold the key to the outcome. Polls show they are significantly more likely than Tories to back Remain, but less likely to take part in the referendum – a recent ORB survey found 52% of Labour voters saying they were “certain to vote”, compared with 69% of Tories and 71% of Ukip supporters.

Cameron, who has been hogging the limelight, is hardly a beguiling poster boy for these people. On Saturday the former Labour leader Lord Kinnock warned: “The risk is, if we get a low turnout, regardless of what people’s background politics is, that by default Leave could win.”

It was no coincidence that Corbyn was in Cardiff. Labour-friendly Wales has turned into one of the most Eurosceptic parts of the UK. Only 37% people plan to vote Remain, according to a recent poll, in what is still a Labour heartland. The impact of immigrants in constituencies like Caerphilly and Merthyr Tydfil and Rhymney has been a siren call to the Brexit campaign, with the government’s apparent impotence in the face of mass job losses at Port Talbot, pride of the Welsh steel industry, hardening many against the establishment in London and Brussels. The improbable election of Ukip’s Neil Hamilton to the Welsh assembly in May is powerful evidence of that.

The key player could be the Labour leader, which might explain his uneven temper. He looks like a man under pressure. And it appeared at first that his temper was set to continue at the podium. “There is a positive case to be made,” Corbyn said. “And I would appeal to the media to report what we actually say, for once, and what the Labour case is.”

He went on to offer evidence of how the EU had benefited the Welsh – £25m for a Welsh government employment programme, £83m for 94,000 apprenticeships, £3.3m for those on long-term sick absence from work – even if some of it was a little niche. “Railway stations across Wales, and I have visited them all, including Aberystwyth, Carmarthen, Llandudno, Pontypridd and Port Talbot, have been upgraded as a result of a £21m cash injection of EU funds,” said Corbyn.

He ended with a rousing climax, firmer than at previous events. “There is an overwhelming case to remain and reform so that we build on the best that Europe has achieved … That is why we established the Labour In campaign, because we have a distinct agenda: a vision to make Britain better and fairer for everyone, by engaging with our neighbours.”

Alison Lyntch, 30, spoke for many in the audience when she said: “On immigration, he doesn’t need to lower his argument to the level of some people. That isn’t to say immigration isn’t important, but there are more significant economic arguments which can win people round. He doesn’t need to be in the gutter.”

I am saying to Cameron and Osborne that it is time for them, the elite, to back off shadow chancellor John McDonnell

The importance of the Corbyn campaign, and the decision by Labour to focus on small town hall meetings, rather than grand setpiece events, isn’t lost on the shadow chancellor, John McDonnell. Interviewed on Saturday, McDonnell gave an ominous warning: “I think it [the referendum race] is close, and the reason is that this establishment campaign is blowing it. The strategy needs to change. Big beasts, largely from the Tory party – political and business big beasts – have imposed themselves on the argument. It’s a bit like the Scottish referendum. People see the establishment ganging up on them, talking down to them. People don’t feel they’re being listened to.”

He called for more town hall events where local issues with the EU could be addressed and concrete solutions provided. And it was time Cameron and his chancellor, George Osborne, took a back seat. “All this hyperbole and exaggeration is undermining the credibility of the argument. People don’t believe what they are being told. There is this negativity. It has proven to be a real turn-off. You can’t frighten people into the ballot.

“It has to be a positive campaign from here on in. And I am saying to Cameron and Osborne that it is time for them, the elite, to back off. I think people are where I am, which is a Eurosceptic position – but not a Euro-exit position. A period of quiet from the likes of Cameron, Osborne and others would be helpful. Let the people speak now.”