Another young person killed in the escalating epidemic of violence. The cause? Take your pick.

The right blames Theresa May for easing up on stop and search for weapons – though she knew there is no evidence that it catches or deters, while it fuels anti-police anger. Others suggest decriminalising drugs would destroy the trade that underpins this mayhem.

Unless you think nothing works, shutting down most youth services, including successful programmes to tackle gang violence, was always likely to ricochet back. Youth services went first in the post-2010 slash-and-burn of council budgets. The young poor were early targets for all benefits cuts: their education maintenance allowance went – up to £30 a week for 16- to 19-year-olds from lowest-income families to keep them in education, covering travel, lunches, books and pocket money. Their families lost child tax credits, child benefit and housing benefit, and were often forced to move and move again.

The best chance of changing life trajectories starts young

Causes are always complex – but does anyone think those cuts had zero effect on young teenagers turning to gangs, drug-dealing and local identity wars, seeking a fleeting sense of respect as so much was taken away? The cynicism of the Evening Standard raising charity funds for child hunger in London and weeping crocodile tears for teenage murders defies belief when its editor, George Osborne, deliberately took most from families with least.

But the best chance of changing life trajectories starts much younger. Today the Sutton Trust has revealed that twice as many children’s centres have closed than official figures indicate: 1,000, with a cascade likely to follow as council cuts bite deeper.

These Sure Start centres were Labour’s flagship community hubs, where families could go right from the birth of their child. They provide help with everything from breast feeding, mental health problems, parenting classes, training for getting jobs, child speech, language therapy and toy libraries.

Those remaining are often hollowed-out shells with one or two weekly sessions, stripped of the professional services that catch problems early. Many parents are expected to travel a long way by bus to reach them. The report’s authors, including Prof Kathy Sylva, are academics who monitored Sure Start centres from the beginning. They found “positive effects on family functioning and home learning environments, that families experienced a less chaotic home life, and that relations between parents and children improved. Mothers using the centres showed improved mental health, and children exhibited greater social skills.”

Counting these closures, Sylva says, “makes you weep.”

The Sure Start idea sprang from landmark US research that followed a group of toddlers through to their 30s. The High Scope scheme, giving deprived children two years of intensive family and pre-school support found that, compared with a control group, many were protected from later disasters. Every dollar spent on this scheme saved $7 later down the line, owing to improvements to crime, mental health and employment.

May pledges herself to the cause of “social mobility”. Her preferred route? Via grammar schools – or, as one Tory put it to me, “picking diamonds from the rough”. The resignation of the chair, Alan Milburn, and the last remaining members of the depleted social mobility commission set up by the Cameron government caused little stir, although the walkout included the former Tory education secretary Gillian Shepherd.

As they left, they cited “lack of progress towards a fairer Britain”, saying they had “little hope that the current government could narrow the gap between the ‘haves’ and ‘have-nots’ ”. Indeed.

Improving mobility without reducing inequality is a nonsense objective. No politician admits that mobility means some moving down as well as up. Few people climb Britain’s tall, steep ladders; while more equal Scandinavians, with a short, flatter ladder find moving up easier, and down less punitive.

Unenthusiastically seeking a new chair for this impossible commission, the government has had to extend the deadline owing to a lack of suitable candidates. Applications finally closed last week: “This is an exciting opportunity to fundamentally shape the social mobility agenda,” says the job ad. The successful candidate needs, “A proven, credible track record of commitment to improving social mobility, and an in-depth and up-to-date understanding of the issues relating to this area.” Plus “experience of working effectively with business.”

Almost by definition, anyone appointed to this post will be unsuitable. Anyone who is clueless to the absurdity of pursuing “social mobility” under government policies that are due to increase absolute child poverty by 4% is either a hypocrite or an idiot, or both.

• Polly Toynbee is a Guardian columnist