When the histories of Theresa May’s time as prime minister are written, many will probably begin with her first words outside No 10, pledging to tackle the “burning injustice” of social stagnation. They will then conclude she failed to do so.

The verdict is one May will find wounding. But the latest “state of the nation” report, published on Tuesday by the Conservative-established social mobility commission, helps ensure it is both inevitable and justified.

The language in the study, which tracks changes – or rather the lack of them – in improved social opportunities between 2014 and the present day, encompassing the end of David Cameron’s tenure and all of May’s, could barely be more blunt.

Inequality is “now entrenched from birth to work”, it concludes, with social mobility stagnating during the period “at virtually all life stages”.

The commission’s work has been a regular headache for the government since it was set up in 2010 under the Cameron-led coalition of the Conservatives and the Liberal Democrats. Alan Milburn, the Tony Blair-era Labour minister who was its first chair, quit along with his whole team in late 2017, saying May was showing no political leadership on the issue.

It has been a long and gradual descent from the heady atmosphere of 13 July 2016, when the May stood outside Downing Street and struck fear into the hearts of many Labour MPs by promising to tackle inequalities and injustices including class, race, gender and age.

“When it comes to opportunity, we won’t entrench the advantages of the fortunate few,” she said. “We will do everything we can to help anybody, whatever your background, to go as far as your talents will take you.”

So what went wrong? In brief: events. Much of the momentum was lost when May inadvertently swapped a small-but-workable Commons majority for a hung parliament in the 2017 election. That reverse prompted the departure of Nick Timothy, one of May’s main advisers, seen as the driver of her social injustice policies.

But more significant than any of that was Brexit, which has stagnated government action in more or less every area beyond the vexed and seemingly endless issue of relations with the EU.

The longer Brexit has gone on, the more this effect has been felt, with the government delaying a new Queen’s speech until a deal is passed, even though ministers have run out of policies to put before the House of Commons. On Monday, May’s spokesman rejected the idea that this was now, in effect, a “zombie government”.

It is notable that for all the tough language in the commission report, there is not a single mention of Brexit in its 156 pages. Even its recommendations are somewhat low key, with ideas such as more funding for further education and for disadvantaged school pupils, and a “review” of children’s centres.

Also notable was that when asked about the commission’s findings, May’s spokesman insisted the prime minister remained committed “to fighting injustice and creating opportunity for everyone”, but cited no new achievements – mainly generalities such as higher employment and wages, and an increase to the national living wage.