There are fears the same thing could happen in the UK. There are more than 260,000 Jewish people living in Britain, or 0.5 per cent of the population, according to the Census in 2011.
Last year saw the most anti-Semitic incidents recorded by police since records began 30 years ago, according to the Campaign Against Anti-Semitism.
On Friday posters advertising a Holocaust memorial event have been daubed with graffiti including the words 'liars' and 'killers'.
Speaking at an event to commemorate the Jewish people who died during the terror attacks in France, Mrs May said: 'The dreadful events in Paris are a reminder of the serious terrorist threat that we face.
'The attack on a Jewish supermarket, where four people were killed, is a chilling reminder of anti-Semitism, not just in France but the recent anti-Semitic prejudice that we sadly have seen in this country.
'I know that many Jewish people in this country are feeling vulnerable and fearful and you're saying that you're anxious for your families, for your children and yourselves.
'I never thought I would see the day when members of the Jewish community in the United Kingdom would say they were fearful of remaining here in the United Kingdom.
'And that means we must all redouble our efforts to wipe out anti-Semitism here in the United Kingdom.'
In the aftermath of the Paris attacks, French prime minister Manuel Valls, who said: 'If 100,000 Jews leave, France will no longer be French, the French Republic will be judged a failure.'
Mrs May said the same sentiment was also true of the UK. 'Without its Jews, Britain would not be Britain, just as without its Muslims, Britain would not be Britain - without its Sikhs, Hindus, Christians and people of other faiths, Britain would not be Britain.'
In solidarity with the French, Mrs May and other attendees of the event held up signs reading: 'Je suis juif' - 'I am Jewish.'
She told the event in London: 'In Europe, of course, we have seen large numbers of Jewish people emigrate and others are questioning their future.
'There have been other attacks as well, the like of which we never thought we'd see again in Europe - in Brussels, of course, where four people were shot and killed at a Jewish museum and in Toulouse, where three children and a teacher were murdered at a Jewish school.
'So I want to say this: Jewish people have long been an important and integral part of this country, we cherish the contribution you make, not just in the past but today and every day.'
Speaking at the same event, Communities Secretary Eric Pickles said that he stood 'shoulder to shoulder with the Jewish community, shoulder to shoulder with fellow British citizens' and described anti-Semitism as 'a cancer'.
He added: 'Modern Britain without a thriving Jewish community would not be Britain. The Jewish community is a vital part of what makes Britain tick, whether it's leadership through business and commerce, arts like dance and literature, or something more humble like members of the JLGB, who give so much to the Jewish community and others.'
The event included a minute's silence for those who lost their lives attended by representatives of CRIF - Conseil Représentatif des Institutions Juives de France, and the French embassy in London. Prayers were led by UK-based French Rabbi Mordechai Fhima.
Board Senior Vice President Laura Marks thanked both cabinet minister for their attendance, saying, 'We so desperately appreciate you both coming along. The support makes so much difference to us.
Vivian Wineman, President of the Board of Deputies of British Jews, said: 'This has been a clear demonstration of the government's and the country's solidarity with the community at this critical
The Association of Chief Police Officers has been reviewing its security measures following the attacks in Paris.
Mr Rowley, a Met assistant commissioner, said in a statement on Friday: 'The global picture of terrorist activity does give us heightened concern about the risk to the Jewish community in the UK.
'We are seeing continuing anti-Semitic rhetoric from extremists and attacks on this community in France and elsewhere.
'In addition to our existing security measures, we are in dialogue with Jewish Community leaders about further actions that we will be taking, including more patrols in key areas.
'We remain alert to the vulnerabilities of other communities. Where we do have particular concerns, we make these known to those involved.'
But David Cameron warned it is impossible to keep people 100 per cent safe from terror attacks in an 'open and free society'.
Meanwhile one of Europe's largest Jewish associations has written a letter to EU ministers asking for gun laws to be relaxed to allow Jews to arm themselves to protect against terror attacks.
Rabbi Menachem Margolin, the head of the European Jewish Association, made the request in the wake of the Paris attacks in which four Jews were killed inside a deli in the French capital.
In the letter, dated January 13, he asks for permission for 'people in the Jewish communities and institutions to own weapons' to protect against 'anti-Semitism, racism, and intolerance'.
- Daily Mail
