The Remain campaign is facing the “very real prospect” of defeat in the referendum in two weeks’ time as it fails to reach traditional Labour voters, Andy Burnham has warned.

The shadow home secretary said a vote to leave the European Union on 23 June could lead to social “fragmentation” and the break-up of the United Kingdom.

Burnham sharply criticised the party’s campaigning, saying it had failed to reach out to traditional Labour voters amid fears that concerns about immigration are driving them to back Leave.

“We have definitely been far too much Hampstead and not enough Hull in recent times and we need to change that. Here we are two weeks away from the very real prospect that Britain will vote for isolation,” he told BBC2’s Newsnight.

“I think it would have a profound effect on our national life – the fragmentation that will come, the fear and the division.

“Those are all the things that the terrorists couldn’t create with their bombs and yet we will have a situation where society becomes more divided.

“If this decision is taken, dominoes will start to fall. It won’t just be the EU that starts to break up, it will be Britain too.”

The warning comes as Ed Miliband tries to inject new momentum into Labour’s campaign effort with an attack on Boris Johnson and the Leave camp for perpetrating a “fraud” on the British people.

The former opposition leader and other senior colleagues will make a series of interventions aimed at winning over wavering Labour supporters.

The former cabinet minister Yvette Cooper will release a report warning of the damage facing Labour heartlands if the “far right of the Conservative party” gets its way.

The Labour deputy leader Tom Watson will release analysis indicating Brexit could result in £18bn of welfare cuts and tax hikes as the Tories impose tighter austerity measures.

The attacks by Labour are aimed at rallying the party’s supporters behind the Remain cause following criticism of Jeremy Corbyn’s efforts in the referendum campaign.

In a speech in London, Miliband will warn that senior members of the Brexit campaign want to abolish measures protecting workers’ rights.

He is expected to say: “The Leave campaign are trying to perpetrate what I can only describe as a fraud on the British people. Tories who in the last days of this contest are trying to disguise themselves in Labour clothes.

“Let’s be clear what the Leave agenda would mean for working people. They want out of Europe so we can be out of the social chapter, as Boris Johnson said in terms in 2012. Their competitiveness strategy for Britain is deregulation and the erosion of rights of working people.”

A Vote Leave spokesman said: “As support drains away from the Remain campaign, they are getting ever more desperate and hysterical with their fanciful Leave predictions.

“We need to vote Leave if we want to take back control of our economy, borders and democracy.”

With Press Association