LONDON — As Britain heads into the last few days of campaigning before the historic referendum on whether to stay in or leave the European Union, only one thing is clear: This will be a narrow, knife-edge, vote.

Just a week ago those pressing for “Brexit” — a British exit from Europe — were ahead in the polls by around five to seven points. But on Sunday the respected polling organization YouGov published two polls showing a swing back to “Remain,” in support of the status quo.

The tragic murder of the MP Jo Cox, a leading figure in the Remain camp, may not have had a direct impact on Sunday’s YouGov polls, given that most of the research in one poll took place before her death. But few British citizens can have heard the words of her alleged killer, Thomas Mair, without a shudder, when he was asked to identify himself in court at the weekend. Instead of giving his name, Mair said, “My name is death to traitors, freedom for Britain.”

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Appalled Jews across the community were united in their response — not just grief for the death of a young woman, but horror at what her murder meant in terms of the European debate.

In the last weeks before the referendum on June 23, the campaign has divided clearly into an at times ill-tempered debate about immigration and its effect on Britain. On the day of Jo Cox’s murder, the right-wing UKIP leader Nigel Farage unveiled a controversial poster denounced as racist across the political spectrum. A picture of Syrian refugees walking into Europe through Slovenia — though not identified as such by UKIP — the clear intention was to fuel a fear of immigrants if Britain stays in Europe.

A Jewish Chronicle poll conducted in May showed that 49 percent of British Jews wanted to remain in Europe. Just over a third of those balloted (34%) backed Brexit, but 17% said at the time that they had not yet made up their minds. Age made a great difference to responses, as younger voters — who have, of course, never known a Britain not in the EU — were keener to remain, while older people, many of whom may have taken part in the 1975 decision to join the European Union, were more supportive of leaving.

West Germany, France and four other nations formed the European Economic Community in 1957, determined to banish forever the bloodshed of two world wars. The grouping became the EU in 1993 and has grown into a 28-nation bloc of more than 500 million people stretching from Ireland to the Aegean Sea, with substantial powers over member states’ laws, economies and social policies. It has its own parliament, central bank and 19 EU members use a common currency, the euro.

Many Britons feel their island nation — a former imperial power with strong ties to the United States — is fundamentally different to its European neighbors. Anti-EU Britons resent everything from fishing quotas to fruit sizes being decided in Brussels.

The anti-EU view is especially strong in the Conservative Party of Prime Minister David Cameron. It was partly to appease his party that Cameron promised to hold a referendum on EU membership by the end of 2017.

Supporters say Britain’s economy and security are enhanced by EU membership. They argue that membership makes it much easier for British companies both large and small to import and export goods to other member countries with minimum hassle. Supporters say being part of the 28-nation bloc gives them many more options and makes it easy for them to live and work in other countries.

Jews in Britain have traditionally been nervous of appearing to speak with one voice on UK politics

Labour Party leaders also argue that European rules and regulations and European courts have improved the way British workers are treated. They say removing these protections could lower living standards.

Jews in Britain have traditionally been nervous of appearing to speak with one voice on UK politics. But when the campaign really got underway in February this year, many Jews were horrified to see their nemesis, the vituperatively anti-Israel politician George Galloway, join UKIP’s Nigel Farage on stage to back the Brexit argument.

Privately, many Jews felt that a campaign backed by both men was something from which they wanted to distance themselves as far as possible. This has continued to be the case despite the involvement of some “Jew-friendly” politicians in the Leave camp such as the outgoing mayor of London, Boris Johnson, and the Justice Secretary, Michael Gove.

European Jews would feel a cold wind on many fronts without the support of their British cousins

For Jews there are three big questions regarding Europe: the attitude to Israel, and the future of shechita (ritual slaughter) and circumcision. Britain’s membership of the EU has allowed this country’s Jewish community to take a leading role in defending all three positions. Though there are 27 member states of the EU, only Britain, France and Germany have significant Jewish populations and the expertise to deal with these challenges. European Jews would feel a cold wind on many fronts without the support of their British cousins.

And British Jews, in the last several months, have had even more reason to wonder about the impact of Brexit, as thousands of French Jews, fleeing anti-Semitism, have made their homes in London. The French Jews are boosting once moribund UK synagogues and giving a new tone to Jewish education — some Jewish primary schools now have near 60% French Jewish children. And what would happen to French Jews in the UK if Britain votes to leave?

Last Tuesday London Jews had the opportunity to hear both sides of the debate as Education Secretary Nicky Morgan went head-to-head with the former Conservative MP Douglas Carswell, who is now UKIP’s only representative in Westminster.

Nicky Morgan is one of Cameron’s closest allies in the Remain campaign but the audience, according to reports, was keener on arguments made by Carswell, who warned of the future of shechita resting in the hands of “faceless bureaucrats” in Brussels and the potential damage done to Israel by EU insistence on specific food labelling.

Morgan attacked Carswell for promoting what she described as a “nasty” and “mean spirited view” on refugees — an argument which has also struck a chord with a community who are overwhelmingly the children and grandchildren of Jewish refugees and immigrants.

The June debate followed one hosted by the Board of Deputies last month, with Daniel Hannan, Conservative member of the European Parliament for South East England, making the case for Brexit, and upcoming Labour MP Wes Streeting (himself a close friend of Jo Cox) speaking on behalf of the Remain campaign.

The European project has brought post-war peace to the continent and relative peace of mind to its Jews. British Jews, buffeted by depression at the anti-Semitic convulsions in the opposition Labour Party, and with a naturally “conservative” with a small “c” bent, are perhaps more likely to stick with what they know and vote to stay in.

However, in Israel, an advocacy group that is allied with the West Bank settler movement is urging British-Israelis to vote in favor of leaving the European Union in Britain’s referendum this week.

Regavim says the European Union is biased against Israel and says voters should oppose the 28-nation bloc and try to weaken it by encouraging Britain to leave. (The EU considers settlements to be illegal.)

Regavim claims that European aid money to the Palestinians has reached terrorists, and that the EU is funding illegal Palestinian construction in the West Bank. It also alleges an EU rule labeling settlement exports to Europe is anti-Semitic, and that the EU funds hostile anti-Israel groups.

There is no denying people’s nervousness and fear of the unknown. A friend applied last month to cash in pension savings and contacted the pensions company when there was no response after six weeks.

“Well,” said a slightly embarrassed official, “it’s the Brexit polls. People don’t know what’s going to happen if we leave Europe so they are trying to get their hands on their money. We can barely cope — we’ve had to take on more staff.”

The first results of the EU referendum will be known when voting closes at 10 pm on Thursday June 23.

— The Associated Press contributed to this report