The national tutoring programme is to be overhauled after criticism of the catchup scheme for schools in England, with the education secretary, Nadhim Zahawi, promising further changes, including shifting funding towards headteachers.

Zahawi said he was transferring £65m away from the NTP, including from Randstad, the Dutch service provider, to schools, in an address at the annual conference of the Association of School and College leaders.

New figures from the Department for Education (DfE) showed that schools undertook the vast majority of catchup tuition under the government’s programme to help pupils recover learning opportunities lost during the pandemic.

“I know that many of you have had challenges with the programme. I have listened and I have heard and we are making improvements as I speak to you today,” Zahawi said. “That includes the immediate transfer of up to £65m into school-led tutoring from the other two routes. It’s become clear to me that by far the most popular route is the one run by the schools.”

Geoff Barton, ASCL general secretary, said: “It has taken far too long for the government to recognise this fact but it has got there in the end. The £65m extra funding announced today will help schools roll out the support that so many children and young people need to recover after two years of learning blighted by the pandemic.”

Zahawi said it was “incredible” that 1 million tutoring courses had began since the NTP was launched in autumn 2020.

The figures from the DfE showed that since September 2021 schools had started 532,000 tutoring courses, while the external tutor-led programme administered by Randstad had provided just 114,000. A further 74,000 courses had been started by school-based academic mentors funded by the government.

The DfE claimed the NTP was still “on track” to meet its target of 2 million courses by the end of the year.

The parts of the tutoring programme administered by Randstad have been heavily criticised for failing to meet targets in enrolling disadvantaged students, thought most likely to have lost out on learning during the pandemic.

MPs on the education select committee on Friday said children in England faced “an epidemic of educational inequality” over the scheme’s failures, and said Randstad should have its DfE contract terminated unless it improved.

The DfE announced further changes to the NTP, including allowing tutors recruited by Randstad to teach up to six children instead of a maximum of three in a group. The DfE also dropped a requirement that academic mentors hired under the scheme needed to be graduates, and now they need only to have A-levels.

Randstad has been approached for comment. In response to the criticism by MPs on the education select committee, it said: “We have been working in partnership with the Department for Education, schools and tuition partners to look at how we can improve the programme moving forward to best serve the needs of schools.”

Zahawi’s speech included insights in the white paper on schools that the government is to publish in the coming weeks.

He said he wanted all schools in England to become academies and join multi-academy trusts: “I see the future as involving all schools being part of a strong trust, and I will say more about this in my white paper.

“What I will say now is that I underline the word ‘strong’, because we mustn’t sugarcoat this – some trusts are not high performing. The white paper will set out how I plan to deal with that challenge as well.”

On Saturday the conference is to be addressed by Amanda Spielman, the head of Ofsted, who is expected to outline her concerns about the recent increase in the number of children in England being home schooled.

“We need to recognise that home education is very hard. Most parents aren’t equipped to do it and if they are motivated by their own or their child’s anxiety, rather than a deeply held desire to home-educate, the outcomes for their child are unlikely to be great,” Spielman will say.