Teachers have gone on strike for a second time at a school rated outstanding by Ofsted, where they say pupils carry knives, threaten staff and fight in the corridors.

Staff at Starbank school in Birmingham, which has more than 2,000 students, said they did not feel safe after receiving physical and verbal threats. The second day of strike action follows a walkout last week, with union members saying the school has not done enough to help teachers deal with poor behaviour.

The NASUWT union, which has 18 members on strike, said not enough progress had been made at a meeting with the local authority on Tuesday.

Chris Keates, the general secretary of the NASUWT, said: “Unfortunately insufficient progress was made at the meeting towards addressing our members’ concerns and, therefore, the strike action planned for Wednesday 3 July will proceed as planned.

“There will be no picket at the school on this occasion as the members will be having a private meeting to review the position, discuss all of the outstanding issues which remain to be addressed, and consider the next stage in the dispute.”

After last week’s strike, the headteacher, Satnam Dosanjh, sent a letter to parents saying pupil behaviour was “well managed” and the school environment “continues to be safe for both pupils and staff”.

Dosanjh wrote that while there had been “isolated incidents of knife possession in school”, they were extremely rare. Panic buttons that were fitted in the school were later removed after teachers claimed that no one responded to them when pressed, according to the Birmingham Mail.

The school in South Yardley, east Birmingham, more than doubled in size in 2016, expanding from a primary school to an “all-through” school with pupils ranging in age from three to 16.

It has been rated outstanding by Ofsted since 2012, and a report last year praised it for its “exceptional ethos, care and quality of education”. The report highlighted that many of the pupils had had a disrupted education, some with no prior experience of formal schooling.

The NASUWT is calling for the school to introduce risk assessments for individual pupils, knife audits and training for staff.

Councillor Jayne Francis said Birmingham city council took all concerns regarding safety very seriously but that visiting council officers had not found any immediate safety concerns at the school. “Issues reported by the trade unions regarding Starbank school have been listened to and actioned,” she said.

“Regrettably, we anticipate a very small number of teaching staff from NASUWT to still take action. We are deeply disappointed with this outcome and with the distraction from the students’ education which this causes.”