More than a million new jobs could be created by 2030 if the UK stays inside the EU, according to Tom Watson. Labour's deputy leader will make the employment plea as his party takes a lead role in the Remain campaign, with just eight days to go before the 23 June referendum.

"Labour is clear that the UK's membership of the EU is good for jobs and good for British workers," Watson is expected to say. "We are united in campaigning for Britain to remain in Europe. That's because Labour values are at the heart of this campaign.

"We believe in standing up for working people whose jobs and communities depend on trade with Europe. We believe in standing up for the rights of everyone to be treated fairly at work, and for the rights at work that are guaranteed by our membership of the EU.

"And we believe in the positive role our membership of the EU can play in the future – the more than a million new jobs our economy has the potential to generate if we remain in the EU, helping to provide opportunities for the next generation."

The comments will come after former Labour prime minster Gordon Brown relaunched the party's pro-EU campaign, amid fears that Prime Minister David Cameron's prominence in the campaign could turn Labour voters off. But Watson himself clashed with Labour leader Jeremy Corbyn over the issue of immigration.

The West Bromwich MP suggested the EU's rules on the issue may have to be revised. "I think a future Europe will have to look at things like the free movement of labour rules," he told the BBC.

Hours later Corbyn rebuked his deputy, pledging to defend the free movement of people principle. "It's intrinsic to the European Union that there has to be free movement of people," the left-wing leader told BuzzFeed News. Immigration has become a top issue in the EU referendum debate, with the Vote Leave campaign backing an Australian-style points system.

The policy had been championed by Ukip and Vote Leave's shift comes after the Office for National Statistics (ONS) revealed that net migration to the UK climbed to 333,000 in 2015 – more than three times Cameron's "tens of thousands" pledge.