The company running the national tutoring programme (NTP) has been axed and funding will go directly to schools instead after the government was forced into a climbdown over its flagship scheme, which will now be overhauled.

Labour accused the government of wasting millions of pounds of public money, and said the NTP revamp announced on Thursday was “too little, too late, for too many children”.

The NTP is regarded by ministers as the jewel in the crown of the government’s £5bn post-pandemic education recovery programme. However it has been the target of widespread criticism after Randstad, the company chosen to provide it, had multiple problems with delivery and scandalously low participation rates in some areas.

After months of negotiations with stakeholders, the education secretary, Nadhim Zahawi, promised a new “simplified” structure to allow extra tuition to reach as many pupils in England as possible.

In a significant U-turn, all of the £349m of tutoring funding for the 2022-23 academic year will now go directly to schools so they can arrange their own provision – something headteachers have been calling for from the outset.

Under its current £32m contract, the outsourcing multinational Randstad plays a central role in the delivery of the NTP, linking schools with approved tuition providers via a platform which has been fraught with problems. It has a “one year, plus one year, plus one year” agreement with the government, which will now be severed at the end of the first year.

Under the new arrangement, schools will be given the freedom to decide how best to provide tutoring for their children, which could include one-on-one or small group tutoring through teachers or teaching assistants, or continuing to work with external tutoring specialists and academic mentors.

The Department for Education (DfE) will launch a procurement process in April for a new supplier for a much smaller contract, which will focus on quality assurance, recruiting and deploying academic mentors, and offering training to support schools to make best use of their funding. Randstad could decide to bid for the new contract.

The move, first revealed by Schools Week, was well received in the sector. “This is a welcome reset of the NTP and kudos to Zahawi for listening,” said one relieved NTP delivery partner.

On funding going directly to schools, Geoff Barton, the general secretary of the Association of School and College Leaders, added: “We have argued since the outset of the programme that this is what should happen.”

Zahawi told Schools Week he did not think it had been a mistake to appoint Randstad. “You launch something, you scale it, and then you begin to circle back and say, right, how can I refine it? And that’s what we’re doing.”

Labour, however, was damning. “The Conservatives’ flagship tutoring programme has failed our children and wasted millions of pounds of public money,” said the shadow education secretary, Bridget Phillipson. “The education secretary is finally catching up but this is too little, too late, for too many children.”

The announcement came as new figures confirmed low participation rates, with just 14% of schools in England accessing tutoring via the Randstad programme this academic year, compared with 53% of schools who arranged tuition themselves through a school-led tuition route introduced last year. Overall, less than 60% of schools have participated in the NTP since September.

Announcing the overhaul, Zahawi said the NTP had transformed the way schools provided support for pupils who needed it most, with 1.2m courses having been started since the programme began.

“It’s teachers and schools that know their pupils best, which is why we are building on the success of school-led tutoring so far – with evidence as our watchword – so that as many children and young people as possible can feel the huge benefits high quality tutoring provides.”

Robert Halfon, the chair of the Commons education committee, welcomed the move, saying: “Randstad’s delivery of the national tutoring programme has been particularly alarming.”

Randstad’s NTP director, Karen Guthrie, said: “We have been lobbying the DfE and ministers for some time to simplify the rules around accessing the programme and standardise the funding and we are pleased that our advice is being implemented for next year.

“We remain committed to the programme’s principles and its delivery and still have an important job to do for the remainder of this year. Randstad will look to continue its relationship with the DfE if we believe it is in the best interest of the programme and all those benefiting from it.”