It is hard to know what is most disheartening at this time of global insecurity: the prime minister’s lackadaisical insouciance, his showy advisers, smug ministers, or the invisible opposition?

This week’s budget should root us back in the domestic arena, so I am going to add my own bete noire: the overused but underscrutinised phrase “levelling up”. We know more about what Dominic Cummings wears and reads than what he and the prime minister mean by it.

In the recent general election, levelling up worked as shorthand for ironing out disparities between the wealthy south and left-behind north, but look more closely and it is clear that some of the most striking inequalities exist within some of the wealthiest areas.

Do poor families in those communities not count? And if they do, levelling up should mean that people have the same chances of a decent education, home, income, status and job, regardless of where they live. Once upon a time this was known as equal opportunities, but like so many good ideas that emanate from the left, this phrase is now ridiculed as being a form of social-engineered levelling down, which is ironic since most of the levelling down in recent years has taken place on the Conservatives’ watch.

Only last month it emerged that some groups are now expected to live shorter lives than they did 10 years ago as a result of growing health inequality. The process of narrowing gaps in educational attainment due to class background is grinding to a halt and will now take 560 years to close, according to the Education Policy Institute, which is urging government not to load the burden of that job on to schools alone.

But schools policy matters, and what little there is at the moment looks sadly inadequate. Alleged levelling up of per-pupil funding over the next three years will still leave huge differences within and between local authority areas.

Many schools are struggling to recruit suitable staff and so are condemned to a vicious cycle of poor results, poor inspection grades and further staffing problems. But where is the plan to level up a pool of excellent teachers in all subjects and all regions?

School admissions practices, an area permanently in need of reform but always off the table, continue to exacerbate inequality, with poorer children clustered in the lower-performing schools and those who are better off able to work the system to their children’s advantage.

Meanwhile, the difference in status between academic and vocational qualifications shows no sign of disappearing as long as FE colleges are underfunded, and all pupils are expected to do mainly academic subjects at GCSE.

Finally, it would be laughable to talk about levelling up without pointing out the chronic unfairness of a system where eight elite schools send more pupils to Oxford and Cambridge than nearly 3,000 other state schools put together.

Shortly after the last reshuffle it was reported that the new cabinet meant a longstanding rivalry between two of those schools – Eton (Johnson) and Winchester (Sunak) – was once again being played out at the heart of government.

Imagine the self-satisfied smirks across sections of the professions where these schools still dominate. The comprehensive school, technical college, non-Oxbridge-educated son of a Pakistani bus driver, Sajid Javid, had been swiftly dispatched, restoring the natural order of their world.

Unfortunately for the government this Eton-Winchester joke shows the real problem with levelling up. The tiny few who dominate society would have to take a step down to give everyone else a chance to progress.

When we have a (preferably female) chancellor and prime minister from diverse backgrounds and non-selective state schools tussling over the future of the country, we might be able to say job done. But the chance of that happening in the lifetime of this government is next to zero.

• This article was amended on 10 and 11 March 2020. An earlier version erroneously said “eight elite private schools” sent more pupils to Oxford and Cambridge than “the remaining 3,000 state schools put together”. That was referring to a Sutton Trust report, which found that eight elite schools (six private and two state), recruited more students than almost 3,000 other UK state schools put together.