Two Steiner state schools in the west of England face possible closure or takeover after the Department for Education said it intended to cut off their funding later this year.

The trusts running the free schools in Bristol and Frome have been issued termination warning notices by the DfE after the schools were rated as inadequate and placed in special measures by Ofsted.

The inspections published in January reported a long list of serious safeguarding and teaching problems at the two schools, which subscribe to aspects of the unconventional educational philosophy created by Rudolf Steiner in the early 20th century.

“I am now issuing this termination warning notice because I do not have confidence that the trust is able to rapidly and sustainably improve the academy’s systems of governance and management and educational standards,” Lisa Mannall, the DfE’s regional schools commissioner for the south-west of England, said in the letters.

“I am therefore minded to terminate the funding agreement of the academy and transfer the school to a strong multi-academy trust that can provide the capacity for continued improvement.”

The letters are the latest step in a formal legal process that could result in the Steiner Academy Bristol and the Steiner Academy Frome being closed unless new sponsors can be found to step in and take them over.

Mannall’s letters told the schools that their safeguarding was not effective, with pupils “exposed to avoidable risk of harm”, including unnecessary physical intervention by staff. The Bristol school was told that bullying was “too frequent” and leaders had been too slow to take action.

“Governors have not held senior leaders to account effectively over time. As a result, teaching is weak and pupils are underachieving significantly across the school,” Mannell added.

Joss Hayes, the headteacher of the Steiner Academy Bristol, said: “External partners have already confirmed that safeguarding is effective at the school. We are committed to making improvements and have started implementing a number of new learning programmes.”

Three of the four Steiner state schools that have opened since 2011 have been rated as inadequate, including Bristol, Frome and a third school in Exeter. The Exeter Steiner Academy was sent a termination warning notice by the DfE last month.

The fourth school, in Hereford, was rated good by Ofsted and posted an encouraging performance in last summer’s GCSE exams.

The trusts in Bristol and Frome have until 20 February to persuade the DfE they have made significant improvements.

Roy Douglas, a governor at the Bristol school, said: “Our parents remains unfailingly supportive of our school and its ethos. We intend to challenge the Ofsted judgement in the courts.”

The governors have begun crowdfunding to pay for legal action, and said they had raised £17,000.

After the Ofsted inspections were published, the education secretary, Damian Hinds, said: “Safeguarding our children and young people throughout their education is paramount, regardless of the setting in which they are being taught.”

Campaigners including Humanists UK have called for the schools to be closed, alleging that the Steiner ethos promotes pseudoscience and homeopathy, including cases of hostility towards vaccinations.