LONDON—The leader of the U.K.’s opposition Labour Party, joined by his senior team and trade-union leaders, issued a rallying cry to supporters on Tuesday to vote to remain in the European Union as the latest opinion polls provide further indications that those campaigning to leave are gaining momentum.
Conservative Prime Minister David Cameron—who is spearheading the push to remain in the EU ahead ofthe country’s June 23 referendum—hasn’t made a significant intervention in the debate since Sunday amid signs that his warnings about withdrawing from the bloc aren’t connecting with some voters, including Labour ones. Some senior Labour figures have in recent days warned that the party had failed to sufficiently reach out to supporters.
Labour Leader Jeremy Corbyn, speaking at a public appearance with senior Labour lawmakers and union officials in London, said the party’s supporters should vote to remain in the EU next week to safeguard workers’ rights, such as working conditions and less discrimination.
“We believe that a leave vote will put many of those things seriously and immediately at risk,“ Mr. Corbyn said. “We urge all of our supporters: Think very carefully about this and vote to remain next Thursday on the 23rd,” he said.
Opinion polls in recent days suggest support has swung in favor of leaving the EU. An EU referendum poll-of-polls calculated by NatCen Social Research, which is based on the average share of the vote for leave and remain in the six most recent polls of voting intentions, shows leave with 51% and remain with 49%, excluding people who are undecided. Three weeks ago, the poll of polls showed remain with 55% and leave with 45%.
Two more polls on Tuesday supported the trend. An online poll of almost 2,500 people, published by TNS Omnibus, put support for leaving the EU in the lead with 35% of the vote, with those favoring remaining at 33%. Adjusted for likely turnout among different groups, the leave camp is projected to get 47% of the vote, while its opponents are seen taking 40%, TNS said.
A survey of 1,002 people carrier out by Communicate Research Ltd. published in the The Sun newspaper’s online edition showed the lead of the remain vote has narrowed to just one percentage point, to 46%—its weakest level since its polling began 13 months ago—from 11 percentage points in May. The poll also showed immigration has grown as an issue and is seen as almost as important as the economy, the newspaper reported.
The Sun, the country’s biggest-selling daily national newspaper, on Tuesday urged its readers to vote to leave the EU, saying it is the country’s last chance to remove itself from “the undemocratic Brussels machine.”
“Staying in will be worse for immigration, worse for jobs, worse for wages and worse for our way of life,” the newspaper said in an article.
News Corp, which owns the Sun, also owns The Wall Street Journal and Dow Jones Newswires.
The varying results of the polls of EU referendum voting intentions, particularly between online and telephone surveys, have fueled debate about their reliability as an indicator. Nevertheless, financial markets have reacted to the recent gains by the leave camp, with the pound weakening amid expectations an exit would hurt the U.K. economy.
Mr. Corbyn has kept a low profile during the campaign relative to Mr. Cameron, which has prompted questions among some analysts and members of the public about his commitment. Mr. Corbyn has said the party backs remaining in the EU but that he remains critical of what he sees as the EU’s shortcomings, and has disputed the government’s warnings of damage to the economy if the U.K. leaves the EU.
Mr. Cameron and other pro-EU campaigners have focused on the economic argument for staying in the EU, warning that exiting could trigger a recession and leave the economy permanently poorer.
Meanwhile, Vote Leave, the official pro-Brexit campaign group, has argued that Britain needs to leave the bloc to regain control over policy-making on immigration and trade, and said the U.K.’s contributions to the EU budget would be better spent at home on institutions such as the state-funded National Health Service.
While analysts have been expecting Labour voters supporters to back EU membership, there are signs some of the party’s supporters are concerned about immigration and its effect on the labor market and public services.
Labour voter Neil Hopkins, 46 years old, who works in a computer-repair shop in the coastal town of Ramsgate, a deprived area about 80 miles east of London, said Labour had sat on the fence on the EU issue. He was planning to vote to leave over concerns that the British government would be unable to control immigration while it remains in the EU and as more countries join the bloc, he said.
“They keep saying that Turkey isn’t going to join but they might not have a choice,” he said on Monday.
In a sign that the Labour leadership is looking to address those concerns, Tom Watson, the party’s deputy leader, told the British Broadcasting Corp. on Tuesday that a future government would have to make a case for revising the EU rules for freedom of movement for workers.
Net migration soared when the Labour government of the day allowed migrants from new EU members Poland and Hungary to work in Britain from 2004, while other EU member states maintained temporary block on their entry. It had predicted just a few thousand would come to Britain from those two countries.
Earlier Tuesday, in a speech after the photo call, Mr. Corbyn lauded the contribution that EU nationals make to the NHS. While EU nationals made up 4.7% of the population, they made up 5% of NHS nurses and 10% of NHS doctors, he said.
Labour has been arguing that withdrawal from the EU would lead to an economic shock that would result in lower tax receipts and lead the Conservative government to introduce more spending cuts that would hit health and other public services.
“I would not be voting for remain if I thought there was any risk whatsoever to our National Health Service,” Mr. Corbyn said. “A vote to leave is a vote that will put the NHS in jeopardy—in the hands of those who want to break it up and end it as a service that is free at the point of use.”
Write to Nicholas Winning at nick.winning@wsj.com
