Theresa May has appointed the Labour MP John Mann as an independent adviser on antisemitism, a critic of Jeremy Corbyn’s approach to handling anti-Jewish hatred.

In one of her last acts as prime minister, May also appointed Imam Qari Asim, the deputy chair of the anti-Muslim hatred working group, as the government’s adviser on Islamophobia to help develop a legal definition after one proposed by MPs and campaigners was rejected by the government.

Mann, who chairs the all-party parliamentary group against antisemitism, will give the next communities secretary advice on antisemitism.

May said Mann was a “key voice on this matter” and had “tirelessly used his role as a politician to speak out on behalf of victims of anti-Jewish racism”.

The outgoing prime minister, who used her penultimate prime minister’s questions to attack Labour’s record in dealing with the issue within the party, said: “Antisemitism is racism. It has absolutely no place in our society and we must fight its bitter scourge wherever it rears its head.

“I’ve been proud to lead a government that is tackling such discrimination in all its forms – from making sure courts have the powers they need to deal with those who peddle hatred, to asking the Law Commission to undertake a full review of hate crime legislation. But there is yet more to do.”

Mann said he would continue to be a strong voice on anti-Jewish hatred. “If we stay silent on the issue of antisemitism, we unwittingly allow cowardice and bigotry to speak its own repulsive language,” he said.

“I will continue to call out those throwing stones of hatred at Jewish people, and will endeavour to give a clarion call to government on prejudice and discrimination on this issue.”

Asim’s appointment comes after the government promised to develop its own definition of Islamophobia, after the communities secretary, James Brokenshire, was strongly criticised for rejecting a definition developed with community groups.

The definition, which has been adopted by Labour and the Liberal Democrats, was set out in a report published by a cross-party group of MPs in December. “Islamophobia is rooted in racism and is a type of racism that targets expressions of Muslimness or perceived Muslimness,” it says.

The row over the definition came in the same month that Conservatives suspended 14 members for allegedly making Islamophobic comments after a string of abusive posts were uncovered on social media.

The inquiry by the all-party parliamentary group on British Muslims held sessions in Manchester, London, Birmingham and Sheffield. Members heard about a wide spectrum of Islamophobic experiences, including multiple incidents of physical and verbal abuse.

Brokenshire said Asim’s work would build on the definitions of Islamophobia being considered, including the APPG definition.

Asim said it was imperative that Islamophobia was defined in order to tackle the rise in anti-Muslim sentiment.

“I am deeply committed to working across Muslim communities and with relevant stakeholders to formulate a legally robust, comprehensive and workable definition of Islamophobia,” he said. “I am honoured to be entrusted with this role, which will have a far reaching impact in protecting British Muslims and tackling anti-Muslim hatred.”

The government said the definition would not be legally binding and would not conflict with equalities legislation.