The social mobility watchdog has accused the Government of quietly dropping the goal of closing the “attainment gap” between pupils from poor families and other children.

The gap will not be narrowed unless ministers make tackling it a top priority, the Social Mobility and Child Poverty Commission chaired by Alan Milburn has warned.

It is alarmed by what it sees as a change of direction by Nicky Morgan, the Education Secretary, who insists the gap should not be “the only focus” and rejects a “lowest common denominator” approach to raising standards.

She said last summer that “true social justice means enabling the very brightest to jump from Bs to As, just as it does getting others from Ds to Cs.”

Mr Milburn, the former Labour Cabinet minister, told The Independent: “The attainment gap between poorer children and their better-off classmates in schools is stubbornly wide. It will close only if the Government keeps it as a top priority for schools. Downgrading it as a focus for schools would be a retrograde step. It would make the Prime Minister’s goal of a One Nation Britain that much harder to achieve.”

In a report to ministers, the commission said poorer children start school almost a year behind their wealthier peers and make less progress than the better off, in effect widening the gap.

It said: “We are deeply concerned at suggestions of a move away from a focus on narrowing the attainment gap, replacing this with an objective of raising standards for all… disregarding the objective at a national level would be a major mistake.”

The advisers added: “The Government’s attention must remain unwaveringly on both raising standards across the board, and on the gap between the richest and the poorest. A move away from this approach would adversely affect both practices and outcomes, and the system itself would fail to fulfil its potential.”

A Department for Education spokesman said: “To suggest that an ambition for all pupils to achieve their potential regardless of background or circumstances is in contradiction with closing the attainment gap is not only incorrect, it just doesn’t make sense.

“We could easily close the gap completely by lowering standards rather than give in to the bigotry of low expectations. We have raised standards and through initiatives like the Pupil Premium – worth £2.5bn this year – we are supporting schools to help every child fulfil their potential.