Take-up of the government’s flagship tutoring programme is so slow that all current secondary pupils in England will have left school by the time the Conservatives finally deliver on their education catch-up promises, Labour has said.

Last summer the prime minister announced 100m hours of one-to-one and small-group tutoring over a three-year period to help pupils in England who have fallen behind in their learning due to the disruption caused by the pandemic.

At the rate of delivery for this academic year, Labour says that figure will not be reached for at least five anda half years, by which time all pupils currently in secondary school will have completed year 11 and moved on.

The national tutoring programme (NTP) was set up with considerable fanfare in 2020 by the former education secretary Gavin Williamson to tackle lost learning caused by lockdown and continuing Covid disruption.

According to Labour’s analysis, 1.2m tuition courses of 15 hours began in the 2021-22 academic year, equating to less than 18m hours in total for the year, meaning that at current rates the 100m hours target will not be met in the next five years.

The Department for Education (DfE) said Labour’s analysis was flawed as the academic year on which it was based was unfinished and its projections were incorrect.

The shadow schools minister, Stephen Morgan, said: “Millions of children will have left school before the government delivers the support it promised. The Conservatives have ducked this generational challenge, leaving children, parents and teachers to pick up the pieces once again.”

The delivery of the NTP has been dogged by problems. Randstad, the Dutch multinational responsible for running the programme, has lost the overall contract for next year, with tuition funding going direct to schools through the schools-led tutoring route, where take-up has been higher.

A DfE spokesperson said: “These projections don’t stand up; they are based on an academic year which hasn’t even finished. The NTP has already delivered 1.5m tutoring courses, with 1.2m courses starting in this academic year alone.

“From next year the NTP will be simplified, with all funding being provided directly to schools, and funding to support education recovery in secondary schools will double.”

The DfE also played down reports that ministers were considering overturning a ban on opening new grammar schools, as did Boris Johnson’s spokesperson, who indicated there was no plan to change policy.

The Telegraph reported that senior government figures were “open” to the idea of looking again at legislation that outlaws any new academically selective schools, amid calls from some “red wall” MPs to bring back grammar schools as part of the government’s levelling up agenda.

The DfE said: “Grammar schools are a valuable part of the school system, with a great ethos, and we want to spread their DNA through the wider education system by encouraging them to join or set up multi-academy trusts. We will protect their selective nature if they do this, but there are no plans to permit the opening of new grammar schools.”

Geoff Barton, the general secretary of the Association of School and College Leaders, said evidence showed that expanding the number of selective schools was not the answer to improving social mobility.

“Grammar schools, where they currently exist, do a great job for their pupils, but so do many comprehensive schools across the country, and the idea that selective education is some sort of golden ticket is, frankly, insulting.”