Analysis: What can Labour do to woo 'weak Leave'?published at 15:44 British Summer Time 14 June 2016
Iain Watson
Political correspondent
The message from Jeremy Corbyn today was that Brexit would be bad for your health - many in the leave campaign, he argued, are no friends of the NHS.
But some in his shadow cabinet believe Labour has to talk more about the issue that's concerning many of their traditional voters: immigration. And those voters have to hear practical proposals. Shadow home secretary Andy Burnham is calling for action to protect the living standards of skilled workers and prevent them from being undercut by migrants.
He told me: "One of the most effective changes that can be done and done quickly is introduce new rules to protect skilled wages because at the moment companies have an incentive to bring in agency staff from around Europe.
"This would be fairer and at the same time reduce the pull factor. It would work by setting clear rules that the going rates for work in the skilled sector cannot be undermined because what we get at the moment is people brought in at the minimum wage that undercut electricians or plasterers or whatever it might be.
"Those are practical policies that would make the free movement we have work more fairly for people."
Another shadow cabinet member told me he was picking up that some of the party's supporters were "weak Leave" and could be brought round to Remain by a clearer and more consistent campaign on issues that concerned them. Others said that voters simply needed reminding that the vast majority of Labour MPs back Remain.
Andy Burnham told me there is still time to win over the sceptics: "There's lots of people out there who still say they're not quite decided and not made up their mind and it’s those people we want to get to and we want to give them the clearest of messages this country's future is better off in the EU."
But his view isn't shared by all senior Labour politicians.
As one senior figure close to the unions put it: "People want change. If Brexit is the only change on offer, they’ll take it."