Labour MPs who voted against a report looking into underachievement among white working-class pupils have found themselves under attack on social media and accused of being “the real racists”.

The report, published by the Conservative-dominated Commons education committee on Tuesday, said schools could be breaking the law by promoting “divisive” terminology such as “white privilege”.

Ian Mearns, Labour MP for Gateshead and one of the four committee members who opposed the final version of the report, said it was clear from the outset that Tory members of the committee were trying to politicise the issue, and he raised concerns about feedback on social media.

In a post on Twitter, Conservative MP Richard Holden (North West Durham) expressed regret that the four Labour MPs voted against what he described as a “vitally important report on educational inequality”. One of the replies to his post says: “Proving that these Labour MPs are the real racists …”.

Mearns said: “The implication was that I was actually being racist against white people. This is the deliberate construction of a political narrative for political gain.”

Fleur Anderson, Labour MP for Putney and another member of the committee, said she was “ashamed” of the way in which the report was framed, pitting disadvantaged groups against each other instead of looking for the roots of that disadvantage.

“I really think in the end when this whole section on white privilege was put in, that’s when the true colours of what some of the Conservative members in that committee wanted to come out of this report. They’ve got a political axe to grind.”

The Social Mobility Commission (SMC), which monitors progress in improving social mobility in the UK, and contributed to evidence gathering for the publication, described the language it used as “awful”.

Sammy Wright, the lead commissioner on schools and higher education for the SMC, acknowledged the report highlighted important issues but said to focus on white pupils underachieving was to put the cart before the horse.

“Many people reading this will identify as white working class and think this is about them – but it’s not. This is about the white poor, and to say that use of the term ‘white privilege’, which has really only become part of the discourse in the last few years, has a role to play is to ignore how long term and systemic these issues are,” he said.

Wright explained that educational underachievement is only part of the picture. Referring to the watchdog’s 2020 report, The Long Shadow of Deprivation, he said they found that, in the least socially mobile areas of the country, even if students got good qualifications they still faced a wage gap of up to a third.

“These groups are economic not ethnic, and working class is not the same as disadvantaged. Using these terms interchangeably is wrong,” he added.

Other critics described the report, which examined why poor white children underperformed compared with other disadvantaged groups, as a “complete whitewash” and the latest attempt by ministers to ignite a culture war.

Nazir Afzal, former chief prosecutor for north-west England, said he was hugely offended by the suggestion that any focus on white privilege contributes to deprived white children being left behind.

“Colour is an additional obstacle that only BAME kids face. A report that fails to put the blame squarely on class differences is quite simply a whitewash,” he said.

Afzal, the chair of a further education college in Rochdale that has a disproportionately high number of working-class children of all races, said there had been decades of underfunding in education.

“Put a black boy in a suit and he will probably fare better than one who can’t afford one, but even he will be more likely to be stopped, arrested, charged and convicted than a white boy in a suit,” he added.

He added: “Working-class children are the victims of government priorities, but black children are also the victims of racism. To suggest otherwise is dishonest.”