New education secretary delivers a blow to hopes she will slow down the government's most controversial changes

Nicky Morgan, the new education secretary, has pledged to carry on the work of Michael Gove by radically expanding free schools, supporting unqualified teachers and keeping changes to the exam system, despite the unpopularity of her predecessor with teachers.

Many in the education establishment rejoiced at the departure of Gove and were hoping the reshuffle would lead to Morgan slowing down or halting some of the government's most controversial changes.

But in her first appearance in the House of Commons, Morgan made clear she admired Gove's legacy and would maintain "undimmed" enthusiasm for free schools – the programme of new state-funded schools built by third parties such as parent groups, education charities or religious groups.

She made the remarks after Richard Fuller, MP for Bedford, said Gove had not been radical on free schools and called for a rapid expansion of the programme across the country.

Morgan replied: "Can I thank the honourable gentleman? It's always very exciting to be tempted and asked to be more radical. Absolutely. I am undimmed in my commitment to free schools and look forward to working with him and members on all sides in getting more free schools up and running."

Tristram Hunt, the shadow education secretary, called on Morgan to "make the break and put the interests of pupils and teachers above Tory party ideology" by ditching the party's commitment to allowing unqualified teachers in free schools. He said Gove was "a man full of ideas – they just happened to be the wrong ones".

But Morgan responded by mocking his "theatricals typical of someone who took part in the Cambridge Footlights as he did". She also accused the history lecturer, who has a doctorate from the University of Cambridge, of being an unqualified teacher himself.

After ignoring the insult, Hunt asked Morgan whether she would slow down the government's "rushed curriculum changes that risk undermining faith in the examination system, causing confusion for pupils and parents?"

"Already Ofqual has warned of greater than normal turbulence in examination results this summer. Is the secretary of state fully satisfied that her government's changes will not compromise fairness and consistency as pupils receive their results in August?" he asked.

Gove argued his changes to the curriculum would make education more rigorous by placing more emphasis on "knowledge-based" exams and less on coursework. His critics accused him of trying to bring them in too quickly, returning to old-fashioned ideas and meddling too much in specifics of what should be taught, such as prioritising British history and authors.

Morgan, who described Gove as "one of the great reforming secretaries of state for education", replied that she was confident in the exam results because a quarter of a million fewer pupils were now in underperforming schools and there were 800,000 more pupils at schools rated good and outstanding.

"That is the legacy left by my right hon friend the member for Surrey Heath [Gove], which I intend to be building on," she said.

Morgan did not comment directly on last week's report about extremism in Birmingham schools, which revealed evidence of "coordinated, deliberate and sustained action to introduce an intolerant and aggressive Islamist ethos into some schools in the city".

The conclusion emerged from a draft of a report leaked to the Guardian, which was commissioned by Gove and written by Peter Clarke, the former head of the Metropolitan police's counter-terrorism command.

Morgan will make a statement in the Commons on the report on Tuesday and told Birmingham Ladywood MP Shabana Mahmood: "There is absolutely no place for extremist views in our schools." She declined an invitation from Liam Byrne, the Birmingham Hodge Hill MP, to apologise for failings by the government to keep schools in the city in check.

Teachers are banking on Morgan to build bridges with their profession after criticism that Gove dismissed much of the educational establishment as "the blob" and pushed through radical changes without listening to warnings about the possible consequences. The Observer reported on Sunday that Morgan rewrote a final ministerial statement from her predecessor to include a promise to listen to their views on schools reform.

The new education secretary has said she will be "nice to teachers", but she made it clear in an interview with the Sunday Times that she would not be "soft-pedalling" in the job.

She also backed Gove's changes that mean parents can be fined for taking their children out of school in term time.

Se said: "For every day or half-day that a child misses [school], it does affect their education. From the prime minister downwards, we have made it clear that being in schools during term time is the best place for children to be. I'm really clear that will continue."