Holland Park School, whose previous pupils include education secretary Nadhim Zahawi, AJ Tracey and the children of Tony Benn and Michael Gove, was one of the most sought after education establishments in the capital.
A group of staff and parents are taking on the school’s governing body, which wants it to join the multi-academy trust United Learning.
Parents and teachers say they have not been properly consulted about the plans, and want the school to join forces with another nearby secondary school.
Michael Wilmott, an National Education Union officer representing staff at the school, told LondonWorld that the NEU has notified the governing body of further strike action.
“We notified the governing body today of six more days of strike action in the autumn term,” he said.
“With regards to having meaningful discussions that could prevent further industrial action, the other side of this has not agreed to meet around the table.
“We are currently in communication with the Department for Education (DfE) and the regional schools commissioner imploring them to have a meeting to discuss how a genuine and transparent consultation process can be conducted.”
The elite state school has also recently come under fire after a culture of bullying and harassment was revealed earlier this year by an internal report.
In May, a summary of an independent investigation released by the school’s governors said there had been a "culture of fear and favouritism".
Kids were allegedly targets of public humiliation and shouting at the school, the investigation found, and there were also safeguarding breaches.
The report also said there had been sexist, Islamophobic and racist discrimination at the school.
The complaints and evidence from the report spanned from 2004 to December 2021.
Ofsted also downgraded the school from "outstanding" to "inadequate" - the worst possible rating - after April inspections.
Colin Hall, the previous headteacher, was the highest paid head of a single academy trust at £280,000-a-year. He was replaced this year by Arwel Jones.
A school spokesman previously said the current governors are “fully committed” to resolving the schools’ problems and to “ensuring that Holland Park School has a positive future in which all students succeed”.
LondonWorld has contacted United Learning for comment.