The scheme is intended to mirror elements of mandatory reporting of the gender pay gap

Employers could be obliged to release their race pay gap statistics under new plans to be unveiled by Theresa May to increase ethnic minority representation in the workplace.

The prime minister will also publish a consultation on mandatory ethnicity pay reporting, marking a year since the government published the findings of its Race Disparity Audit on how people of different ethnic backgrounds are treated across society.

Public services including the NHS, armed forces, schools and the police force will be told to set out plans on how they will increase the proportion of leaders from ethnic minority backgrounds.

The announcement came as May was challenged by a leading Labour MP to prove her public commitment to social equality by enforcing a measure that would oblige public bodies to take account of social disadvantage when considering policy.

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Harriet Harman said that if May took no action on a section of the 2010 Equalities Act that was passed under Labour, then shelved by David Cameron’s government, it would show that her words on social injustice were “just crocodile tears”.

The prime minister’s new commitments on ethnic equality will also see a so-called race at work charter, signed by high-profile public bodies and businesses including NHS England, Lloyds Banking Group, Saatchi & Saatchi, KPMG, RBS, the civil service and advertising agency WPP.

As part of the consultation on the race pay gap, employees will be asked to share their views on mandatory pay reporting. The government has admitted that the number of organisations publishing the information voluntarily remains low.

The race pay gap reporting is intended to mirror elements of the gender pay gap regulations, proposing the same threshold of 250 employees or above for mandatory reporting.

Earlier this year an audit launched by London’s mayor, Sadiq Khan, found that the city’s black and minority ethnic public employees were paid anything up to 37% less on average than their white counterparts.

Announcing the new scheme, May said too often minority employees “feel they’re hitting a brick wall when it comes to career progression”. She said: “Our focus is now on making sure the UK’s organisations, boardrooms and senior management teams are truly reflective of the workplaces they manage, and the measures we are taking today will help employers identify the actions needed to create a fairer and more diverse workforce.”

Harman’s challenge to May on social equality comes in a lecture she is due to give on Thursday in Grimsby in commemoration of Anthony Crosland, the late Labour minister who represented the town in parliament for 18 years.

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In the talk, Harman will describe how Cameron mothballed clause one of the Equalities Act, which would oblige public bodies to act in ways that would “reduce the inequalities of outcome which result from socioeconomic disadvantage”.

“Theresa May, in her first speech as prime minister on the steps of Downing Street, spoke of how she was determined to tackle what she called the burning injustice,” Harman plans to say. “But under her government, it’s getting worse. And, as has always happened with a Tory government, the possibility of those born at the bottom to rise up the ladder is becomes more remote.”

Harman will add: “So my challenge to the prime minister is, if you mean what you say about tackling those burning injustices, if you are genuine in wanting to tackle lack of social mobility, then implement clause one.”

Meanwhile, Labour has announced plans to boost teaching connected to black history in schools, along with the history of the British empire, colonialism and slavery.

On a visit to Bristol marking Black History month, Jeremy Corbyn was to argue it is “vital that future generations understand the role that black Britons have played in our country’s history and the struggle for racial equality”. He was to say: “In the light of the Windrush scandal, Black History month has taken on a renewed significance and it is more important now than ever that we learn and understand as a society the role and legacy of the British empire, colonisation and slavery.”