Nick Timothy, who quit after election, denies he was behind departure of Justine Greening as education secretary

Theresa May’s former chief of staff has been accused of meddling in education policy after he claimed Justine Greening had to be sacked because she had blocked attempts to reduce university tuition fees and frustrated schools reform.

Nick Timothy, who left his job after the Conservatives lost their majority in last year’s election, attacked Greening’s approach to the education portfolio in a column for the Telegraph. He denied he had got her sacked but said he agreed with May’s decision to remove her from the role.

However, Greening received support from a number of former colleagues, including Jo Johnson, who was universities minister until he moved to a new role in the reshuffle.

“So wrong, this stuff re Justine Greening – she supported me in every single reform we undertook of our universities, was a terrific colleague and faultlessly loyal,” he tweeted.

Anna Soubry, the outspoken former business minister, tweeted: “Disappointed and surprised the man who helped lose us our majority & was sacked from No 10 is still in charge.”

In the column, Timothy claimed Greening blocked proposals to reduce interest rates on student loan repayments and allow institutions to charge different fees. He said the ideas could be revived by the government after this week’s reshuffle, in which Greening resigned after refusing to move to a different department.

Timothy denied any involvement in Greening’s departure but said she had “put the brakes on policies that work”.

He wrote: “Young people must be given better choices at 18. Right now, the incentives tell them to go to university. Many emerge with good degrees, but others come out with a costly qualification that makes little difference. On average, they will graduate with debts of £50,000, the highest in the world. Those who do not go to university – still more than half of young people – are neglected by a system guilty of institutionalised snobbery.”

Timothy urged the new education secretary, Damian Hinds, to support the prime minister’s universities policy review.

“Greening blocked proposals to reduce tuition fees and refused to hold a proper review of tertiary education. Hinds must be brave enough to do that, to ensure universities are better, fees are lower and young people get the technical or academic education that suits them. He is already touted as a potential future prime minister: if he gets this right, he will be a convincing candidate for the job,” he said.

Higher education policy is rumoured to be an important part of May’s plan to win back young voters, who overwhelmingly backed Labour in last year’s election.