Labour will promise extra support for communities facing pressure from migration as part of a push to mobilise the party's traditional supporters around staying in the EU.
Gordon Brown will lead the charge amid fears large numbers are being lost to the Brexit camp over warnings of the threat to jobs and public services from unlimited access to European workers.
Read more: Bullying-accused David Cameron says he has duty to warn of Brexit dangers
The former Prime Minister said the positive case for a Remain vote had been squeezed out by media coverage of bitter fighting between rival Tories and urgently needed to be made to show people would be "better off".
Shadow chancellor John McDonnell said the party had 10 days to "save" the campaign.
Prime Minister David Cameron and other prominent Conservative pro-EU figures are expected to take a back seat in a co-ordinated effort to shift the focus of the fight and woo undecided voters.
"It is time now for us to step our efforts up," Mr Brown told the Sky News Murnaghan programme - saying the party had drawn up "detailed proposals" to put to the country in the closing days of the campaign.
Read more: This is an ex-project - John Cleese blasts EU and backs Brexit
"We have got to show people the positive benefits - that you are not voting for the status quo, you are not voting for insecurity.
"You are voting for a future where we can make jobs more secure, where we can create more jobs by changing the single market, we can improve people's quality of life, we can improve workers' rights.
"Once we set out this agenda I think you will see Labour voters far more enthusiastic about a vote to Remain."
He said Labour's pitch would include "how we relieve the pressure in communities where there have been high levels of migration" through specific financial support from Brussels for schools and the health service.
His leading role as chancellor in keeping Britain out of the euro single currency showed, he suggested, that he was able to "get this balance right" between co-operation with European neighbours and keeping control of the most important decisions.
Read more: Brexit war among the Benidorm Brits
Mr Brown said the real problem was illegal immigration and warned the UK "cannot afford to walk away" from the co-operation needed to stop people smugglers and criminal gangs.
"In the end, people are patriotic British citizens. They are proud of our country and they are proud most of all when we lead, not stand apart, not standing outside isolated as some would want us to do."
Labour leader Jeremy Corbyn has been accused of only lending lukewarm support to the In campaign - giving his commitment to the cause a seven out of 10 in an interview on Channel 4's The Last Leg.
Deputy leader Tom Watson said it was important for him to be seen to get the message across because he was far more "in tune with most normal people" and "cuts through to young people in a way few people can".
He told BBC Radio 5's Pienaar's Politics that "like most Labour voters" Mr Corbyn had significant criticisms of the EU but wanted to stay in and see it reformed.
Far from being split, he said: "I can't think of an issue that has united the Labour Party at any point in my life more than this.
"He could not be clearer: He wants Labour supporters to remain in the EU and I am sure you are going to hear that message all the way through to June 23."
Mr McDonnell told ITV's Peston on Sunday programme: "I want to stay within but I want it to be Labour voices now in this next 10 days to save this campaign because up until now all we've heard is Conservatives fighting amongst themselves who seem more interested in who's the leader of the Tory party than they are about the future of our country."
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