HASTINGS, England (Reuters) - It doesn’t take much for Britain’s main opposition leader, Jeremy Corbyn, to win a cheer from his Labour Party faithful -- the ovations the left-wing leader gets for his promises to build a fairer society have become the stuff of political lore.

Jeremy Corbyn, Leader of the Labour Party pauses as he gives a speech days after he called a vote of no confidence in Prime Minister Theresa May's government, in Hastings, Britain, January 17, 2019. REUTERS/Peter Nicholls

But in the English seaside town of Hastings on Thursday, another message drew an almighty roar of approval -- that his party might look at a second referendum on Brexit.

The prospect of holding a second referendum on leaving the European Union poses a particular challenge for Corbyn: while many of the party’s members fervently back it, others just want to leave as soon as possible.

Like the rest of Britain, Labour was deeply divided by the June 2016 referendum on membership of the EU in which 52 percent voted to leave and 48 percent backed remaining in the bloc.

Sources in Labour suggest that a second referendum -- backers call it a “People’s Vote” -- is something Corbyn would do almost anything to avoid. So far, he has kept the option open while being clear that he would prefer other alternatives, such as a new election or Labour’s own plan for leaving the EU.

“All options are on the table. We’re serious about finding a way through,” he told several hundred supporters in a meeting hall in a former church on the southern English seafront.

“Our first option is the alternative plan we have laid out over the past year ... But if the government remains intransigent ... and the country is facing the potential disaster of ‘no deal’, our duty will then be to look at other options ... including the option of a public vote.”

That drew cheers from a crowd which also applauded Corbyn’s plan not to speak to May to find a way to break the deadlock in parliament on Brexit unless the prime minister rules out leaving the EU without an agreement -- the ‘no deal’ option.

May has adamantly rejected any new vote that would allow an option to halt Brexit. The prime minister says a failure to deliver the outcome of the 2016 vote to leave would be “catastrophic” for British democracy.

Nevertheless, backers of a new referendum say it would be possible to force one, if Corbyn were finally willing to throw the support of the main opposition party behind it.

Although Corbyn campaigned to remain in the EU in 2016, some of his critics within the party say he was only ever a lukewarm supporter of it. He voted against joining the European project in the 1970s and criticised it from the left for decades.

Labour sources say Corbyn’s reluctance to support a second referendum comes from a fear not only of alienating Labour voters mainly in northern and central England who backed “leave”, but also concern about widening rifts in the country.

“SPLINTERS”

In a week when May’s plan for Brexit was crushed in parliament and Corbyn’s bid to force a national election failed, many in the party say the time to put off a decision has now run out. David Lammy, a prominent Labour supporter of a new referendum, said that if Corbyn sits on the fence, he “will get splinters in places he doesn’t want”.

Three of Britain’s four living former prime ministers say a People’s Vote is the only way to break the deadlock. A poll this week found Britain would back staying in the EU by a 12 percentage point margin.

But for Labour’s leadership, the idea of a second referendum poses serious problems -- it could alienate “leave” voters in the next election, who form a majority in many of the constituencies Labour would need to win to take power.

Only 71 of the 256 Labour lawmakers signed a letter to Corbyn this week calling on him to back a new vote, and J.P. Morgan analyst Malcolm Burr noted that even if Corbyn ordered his party to back it, some of his lawmakers would still balk.

“We find it difficult to see Labour support for a second referendum rising above 200 votes,” Burr said, noting that this would mean 65 Conservatives would have to be won over. He put the odds of a new referendum at just 25 percent.

Still there is continued pressure, from other opposition parties and from business. In a letter on Wednesday after the Conservative government defeated Corbyn’s no-confidence motion which could have triggered an election, leaders of the smaller opposition parties wrote to ask Corbyn to back a new referendum.

“Following this evening’s unsuccessful vote of no confidence in the prime minister, which we all supported, we are writing to implore you to adopt as party policy a People’s Vote on the final Brexit deal,” wrote parliamentary leaders of Scottish and Welsh parties, the pro-EU Liberal Democrats and the Greens.

More than 100 bosses of smaller British companies including in media, design and architecture also said the only way to stop the country from “crashing out of the EU with no deal” would be to ask “the people whether they still want to leave the EU”.

“With the clock now ticking rapidly before we are due to quit, politicians must not waste any more time on fantasies,” they wrote in a letter.

But for now, Corbyn is still in no hurry to pick sides.

“We are the party that has consistently sought to bring people together, to find a way through that respects people’s concerns whichever way they voted in the referendum,” he said.

“Because I believe that the real divide in our country is not between leave and remain,” he said, shifting to a Labour Party slogan: “It is between the many and the few.”