Protesters who are boycotting Israeli goods over Gaza need to be reminded that the Nazi campaign against Jewish goods ended with a campaign against Jewish lives, senior Tory Michael Gove has said.

Warning of a "resurgent, mutating, lethal virus of antisemitism", the Conservative chief whip also claimed those who compare Israel's actions to Nazi war crimes are engaging in a form of Holocaust denial.

Gove made his intervention in a speech at the Holocaust Education Trust on Tuesday night, in response to findings that there had been a fivefold increase in antisemitic incidents in the wake of Israel's latest conflict with Hamas.

Israel's actions in Gaza provoked an international outcry, with the UN condemning the shelling of a school as "a moral outrage" and the US calling it disgraceful. There are several campaigns that urge people to shun Israeli produce, including Jews for Boycotting Israeli Goods and the Boycott, Divestment and Sanctions movement.

But Gove criticised the boycotts of Israeli goods and warned too many people are now conflating legitimate criticism of Israel's general policies with straightforward antisemitism.

He said a line has been crossed when banners at pro-Palestinian rallies carry slogans such as "Stop Doing What Hitler Did To You" or "Gaza is a Concentration Camp". Lord Prescott, the Labour peer and former deputy prime minister, is among those who have previously been criticised for comparing Gaza to a concentration camp.

Citing a historian, Professor Deborah Lipstadt, Gove said there appeared among some opponents of Israel's actions to be a "deliberate attempt to devalue the unique significance of the Holocaust, and so remove the stigma from antisemitism".

"And even as this relativisation, trivialisation and perversion of the Holocaust goes on so prejudice towards the Jewish people grows," Gove said.

"The Tricycle theatre attempts to turn away donations which support the Jewish Film Festival because the money is Israeli and therefore tainted. In our supermarkets our citizens mount boycotts of Israeli produce, some going so far as to ransack the shelves, scatter goods and render them unsaleable. In some supermarkets the conflation of anti-Israeli agitation and straightforward antisemitism has resulted in kosher goods being withdrawn.

"We need to speak out against this prejudice. We need to remind people that what began with a campaign against Jewish goods in the past ended with a campaign against Jewish lives. We need to spell out that this sort of prejudice starts with the Jews but never ends with the Jews. We need to stand united against hate. Now more than ever."

Gove listed a number of antisemitic incidents that have occurred across Europe over the past few months, calling on people to "remember where this leads". There has been "insufficient indignation" about growing anti-Jewish prejudice, he argued.

"In France, in July of this year more than 100 Jewish citizens had to be rescued from one synagogue and another was firebombed. The leader of an antisemitic party – the Front National – is France's most popular politician. Heroes of popular culture, like the comedian Dieudonné M'bala M'bala, try to make hatred of Jews a badge of radical chic," he said.

"The virus is spreading across other European nations. In Germany, Molotov cocktails were lobbed at one synagogue. In Belgium, a cafe displays a sign saying 'dogs are allowed but Jews are not', while a doctor refuses to treat Jewish patients. And in May of this year four people visiting the Jewish museum in Brussels were killed by a jihadist terrorist."

Arguing that the UK and Israel have a common cause, Gove said: "We know that the jihadist terrorists responsible for horrific violence across the Middle East are targeting not just Jews and Israelis but all of us in the west.

"They hate Israel, and they wish to wipe out the Jewish people's home, not because of what Israel does but because of what Israel is – free, democratic, liberal and western. We need to remind ourselves that defending Israel's right to exist is defending our common humanity. Now more than ever."

On Monday, David Cameron spoke out in parliament about his deep concerns about "growing reports of antisemitism on our streets in Britain".

The prime minister said: "Let me be clear, we must not tolerate this in our country. There can never be any excuse for antisemitism, and no disagreements on politics or policy should ever be allowed to justify racism, prejudice or extremism in any form."

Cameron has always said his belief in Israel is unbreakable and he has strongly supported the state's right to defend itself against the rocket attacks of Hamas. However, he said the UN was right to speak out against Israel's school strike and last week condemned the country's appropriation of 1,000 acres of Palestinian territory as "utterly deplorable".