Alan Johnson has said pro-Europeans have an "obligation" to warn voters about the dangers of Britain leaving the EU, amid accusations they are "peddling fear".
The former cabinet minister who is leading Labour's 'In' campaign also said it was up to
Corbyn how much he wanted to throw himself into the referendum.
Following a speech at the Chatham House think-tank in central-London on Tuesday evening, Johnson said he expected the 'Out' campaign to take the lead in the polls at various points.
"I wouldn't be surprised if things moved about a bit," he said when asked if 'Out' could take the lead at some point before the vote.
Johnson added he would happily take a repeat of the ten-point victory secured for the United Kingdom at the Scottish referendum.
Last week the umbrella Britain Stronger in Europe campaign launched with a warning from Sir Hugh Orde, the former head of the Association of Chief Police Officers, that criminals would see Britain as a safe haven if it quit the EU.
The warning was greeted by some as evidence that the 'In' campaign intended to repeat the so-called 'Project Fear' strategy deployed by the Better Together campaign in the Scottish referendum.
However Johnson said it would be a mistake not to raise concerns about what would happen in the event of Brexit.
"People will say we are peddling fear. There will be a lot of commentary to say we shouldn’t be talking about the weakest argument that the 'No' vote have, which is, what is the world going to be like for us if we go into isolation?" he said.
"What are we going to be, the 51st state of America? Are we going to be a free market off-shore Singapore in Europe? Are we going to be this sepia tinted world of the 1950s?"
Johnson said: "No one can argue that people don’t know what it's like to be in the EU. They have had experience of being in, they don't know what its like wrenching themselves away. We have an obligation to make that argument."
The veteran Labour MP said the strategy was "a much stronger argument, incidentally, probably, than we even had in Scotland" as the unionists "won a referendum by 10%".
He added: "I would take 10% for staying in EU as a significant victory."
Johnson is an ardent pro-European. However Corbyn, who voted to leave Europe at the 1975 referendum, was somewhat ambivalent about Britain's membership of the EU during the leadership contest.
The former cabinet minister insisted Labour was committed to EU membership. He said the decision at Labour's conference last month to withdraw a proposal that the party re-examine its position on the referendum once David Cameron returned with his renegotiated deal showed the party was "unified" on the issue of Europe. "We ended up united on this," he said.
He added he was "satisfied" it was a position Corbyn shared. However he said it was up to the Labour leader to decide how much he got involved in the campaign.
He told The Huffington Post UK: "Jeremy Corbyn may well have noted 'No' in 1975, in musical terms I was discovering Bruce Springsteen and he was probably still listening to the Incredible String Band.
"But he was very clear we are better off inside Europe and the things we don't like we are better off having influence over rather than walking off the pitch.
"I am leading the campaign, how Jeremy, Tom Watson, other members of the shadow cabinet participate is up to them."
Johnson said the campaign to stay in the EU should be "bottom up" and not be led by "blokes like me in suits".
"It needs to be local people, university professors, clinicians, hairdressers postmen and postwomen making the arguments."