Thomas Mair was repeatedly described as a "hero" and a "patriot" online after he murdered Labour MP Jo Cox in June.

Analysis of 52,000 abusive tweets from 25,000 individuals prompted calls for social media companies to do more to tackle hate speech on their sites. Researchers revealed common words associated with Cox and Mair, now jailed for life, included "white power", "rapists", "traitor", "patriot" and "hero".

The findings by academics Dr Imran Awan of Birmingham City University and Dr Irene Zempi of Nottingham Trent University come ahead of a government report on integration to be unveiled next month.

Louise Casey's report will claim the idea of integration has broadly failed with Islamist and far-right extremists both allowed to gain traction, according to the Guardian.

The analysis of social media released on Monday by anti-fascist charity Hope Not Hate found a key theme to emerge was Jo Cox "deserved to die" because "she supported rape gangs", referring to child sexual exploitation scandals in Rotherham, South Yorkshire.

The report called for social media training in schools and for companies such as Twitter, Facebook and Google to sign a duty of care for users.

"The authors feel that social media companies must be more proactive in responding to online hate crime," the report read. "This includes working alongside the Crown Prosecution Service (CPS) and prosecuting those who are responsible for posting, sharing and endorsing harmful content."

Chief executive Nick Lowles said: "Mair acted alone but he was inspired by over 30 years of reading Nazi propaganda.

"Clearly there were those on social media and other digital platforms who sought to exploit and profit from his disgusting actions, and the tensions also arising from the referendum process, to spread their vile beliefs."

He added: "It is time for the authorities to take greater note of these ideologues of hate, and time too for social media companies – and Twitter in particular – to up their game when it comes to providing a safe platform for expression.

"Free speech does not equal hate speech, which can have very real consequences and impact in communities in the UK."

The report on Monday comes after Westminster party leaders were told to tone down rhetoric that "polarized" the country and "legitimized hate".

David Isaac, chair of the Equality and Human Rights Commisison, signed the letter and called for "accurate information and respectful debate" from politicians.

"We are concerned that attacks on supporters of both sides of the Brexit debate have polarised many parts of the country," he said.

"There are those who used, and continue to use, public concern about immigration policy and the economy to legitimise hate.

"The vast majority of people who voted to leave the European Union did so because they believe it is best for Britain and not because they are intolerant of others."