The governors of Saltley school, one of the Birmingham schools placed in special measures after an investigation into an alleged plot involving Islamist extremists, have resigned in protest at the way their school has been treated by Ofsted and Birmingham council.

The mass resignation is the first significant response by the governing boards of the five schools at the heart of the "Trojan horse" affair, which are awaiting publication of reports by Peter Clarke, the former Metropolitan police counter-terrorism commander commissioned by the education secretary, Michael Gove, to investigate allegations of extremism, and by Birmingham council.

"As a governing body we have no faith or trust in the impartiality of Ofsted, the competence of the local authority and express grave concern in the way that the secretary of state [Michael Gove] has described communities as 'swamps' and made it appear that any expression of Muslim piety is a stage in the radicalisation of young Muslims," the governors said in a statement. "Though we have challenged both the way the Ofsted inspection was carried out and the conclusions it came to, the governing board has no resources to take this further – therefore we have decided to resign in protest."

The move leaves the secondary school of nearly 1,000 pupils in Bordesley Green, east Birmingham, without governors at a critical time, with a month remaining until the end of the school year.

Saltley is the only one of the five schools placed in special measures by Ofsted that remained under the auspices of the local authority.

A spokesperson for Birmingham council said: "We had made clear our intention to work with the school and the DfE to seek to put in place an interim executive board as part of the response to the school being placed in special measures. We share the commitment of the outgoing governors to the success of young people in Saltley school and are very determined to see this school return to being the good school it once was as quickly as possible."

The departing governors wrote a detailed response to their inspections by Ofsted and their treatment at the hands of the Department for Education (DfE), rebutting several points and arguing that the findings were unsubstantiated and that the inspection process was flawed.

"We have been left with little faith or trust in either the impartiality of Ofsted or the competency of the local authority. We have deep concerns for the future of our communities and young people following the actions of the secretary of state for education in the manner this whole process has been conducted and to what cost," the governors said in their resignation statement.

An Ofsted inspection before the Trojan horse letter appeared last year found a breakdown in relations between staff and governors. This month's Ofsted report found: "Neither leaders nor governors have an accurate view of the school's strengths and weaknesses. As a result, they are unable to plan and deliver work to improve the school."

In a separate development, John Hemming, the Liberal Democrat MP for Birmingham Yardley, has offered to take over as chair of governors at Oldknow academy, a primary school in his constituency that was inspected in connection with the Trojan horse investigation.

Hemming said that he has spoken with the current board of governors at the school as well as the DfE. "I've talked to stakeholders to see if I can help to offer a solution," he said.

Oldknow made headlines this month when separate reports by Ofsted and the DfE described a string of events – including spending £50,000 on a school trip to Saudi Arabia for Muslim pupils, and intimidation of staff – that saw the school placed in special measures.

Oldknow has been given 30 days notice by the DfE to formulate a response to the criticisms levelled by the inspectors. But when the notice period expires on 4 July the DfE is likely to terminate the school's funding agreement and impose new management.

In 2012 the school was rated as "outstanding" by Ofsted, and it converted to academy status. Even after the recent inspections, Ofsted still rates the school as outstanding for teaching and pupil achievement, although it was rated as "inadequate" for pupil safety and leadership.