The Tory-Liberal Democrat coalition has descended into open warfare over education policy as Nick Clegg dramatically disowned the "ideology" driving much of Michael Gove's controversial schools reform programme.

In a speech this week, extracts of which were released on Saturday night, the deputy prime minister will say that unqualified teachers should not be allowed to teach in state-funded schools and that parents need more reassurance about standards and the curriculum. "Parents don't want ideology to get in the way of their children's education," he will say.

The intervention by Clegg drives a wedge between the two governing parties over a key domestic policy, as more signs of trouble emerge this weekend with the free school programme, the flagship of the Tories' public service reform agenda.

The Observer can reveal that a second unqualified headteacher of a free school has quit her post following criticism. Last week the Guardian revealed that Annaliese Briggs, a 27-year-old who was unqualified when she was appointed as headteacher of Pimlico free school in London, had resigned after just three weeks in the job.

Now it has emerged that Lindsey Snowdon has stepped down from the Discovery new school in Crawley, West Sussex, after a stinging Ofsted report into her work at the 60-pupil primary free school, saying she "lacks the skills and knowledge to improve teaching".

A temporary head, experienced in turning round "failing schools", has been appointed in her place.

Gavin Gordon, a parent who took his son and daughter out of the school last year because he was so displeased with it, said: "My children were not getting the teaching they deserved and that we were promised. On reflection I think one of the reasons was that the teachers were not trained. And you could not complain to anyone. It was all run by the same family."

Last week a 400-pupil Muslim secondary school in Derby, the Al-Madinah free school, was condemned as "dysfunctional" by Ofsted and received the lowest marks in every category from inspectors who were severely critical of the lack of training received by its teachers.

In Clegg's speech he will respond to the growing worries over free schools, saying that while he is in favour of more autonomy, there have to be national standards and controls that parents can rely on. Until now the Liberal Democrats have kept to a fragile truce with the Tories over school reform.

Addressing the issue of unqualified teachers, Clegg will make clear that anyone teaching in a state school should be fully qualified, or be working towards a full qualification. "Frankly it makes no sense to me to have qualified teacher status if only a few schools have to employ qualified teachers," Clegg will say.

"Over the last 10 years, there's been a revolution in the way in which we've recruited and trained our teachers. Whether it's through the on-the-job learning offered through schemes like Teach First and Schools Direct or the continued contribution of our universities to educating generations of Britain's teachers." He will add: "That's why I believe that we should have qualified teachers in all our schools."

Tristram Hunt, the shadow education secretary, said: "I'm delighted Nick Clegg has realised the dangers of an ideologically driven schools policy. We would be happy to work with him to reintroduce accountability, proper standards and qualified teachers in all our schools across the country."

Gove's department says that headteachers of academies or free schools should have the freedom to employ untrained teachers in the same way that private schools "hire the great linguists, scientists, engineers and other specialists they know can best teach and inspire their pupils".

Clegg will also call for the national curriculum and rigorous new food standards to apply in all schools, rather than just those that remain under local authority control. "What is the point of having a national curriculum if only a few schools have to teach it? Let's teach it in all our schools," he will say.

The Observer has also learned that senior officials at the top of Ofsted are growing increasingly worried about the effect that unqualified teachers could have on individual schools and the reputation of academies and free schools.

One high-ranking source said: "It is taken as a given [at Ofsted] that everyone believes teachers should be qualified or in the process of being qualified. It is assumed that that is what everyone thinks so it is not openly discussed, but it will be tackled when we publish our annual report in November."

Last year the head of Ofsted, Sir Michael Wilshaw, made clear to a Commons committee that he believed teachers should be qualified: "I would expect all the teachers in my school to have qualified teacher status," Wilshaw said.

An Opinium/Observer poll finds that while twice as many people think free schools are a good idea as those who don't, 60% of people are concerned at the prospect of unqualified teachers being employed in them.



• This article was amended on 20 October 2013 to clarify that Briggs was unqualified when she was appointed as headteacher of Pimlico free school. She was awarded a PGCE in July 2013, after the appointment was made.