The government’s chief adviser on extremism has called for a clearer official definition of extremism in the light of revelations that Extinction Rebellion and other non-violent groups have featured in counter-terrorism materials.

Against a backdrop of increasing political pressure to investigate the error, Sara Khan, who leads the commission for countering extremism (CCE), said police chiefs were right to recall guidance that batched XR alongside violent neo-Nazis and jihadists.

Her intervention came as the interim leader of the Liberal Democrats, Ed Davey, wrote to the home secretary, Priti Patel, demanding an update on the independent review of the controversial anti-radicalisation programme Prevent and calling for the latest revelations about XR to fall under its remit.

The future of the review has been left in doubt after its chair was forced to step down last month.

Earlier this month, the Guardian revealed Extinction Rebellion featured on a list of extremist ideologies that should be reported to authorities running Prevent. Police chiefs said including XR was an “error of judgeent”, recalled the guidance and launched an internal review.

Since then, teachers, council officers and other public sector workers have come forward to share their own experiences of Prevent training in which XR and other non-violent groups featured.

Sara Khan, the lead commissioner for countering extremism, said: “It is right that CTPSE (Counter Terrorism Policing South East) have recalled their guidance on Extinction Rebellion. Our police, security and statutory bodies have a duty to assess complex risks every day to protect the young and vulnerable from extremism which can present itself from a diverse range of ideologies as our work has shown.

“I believe it is in our country’s interest that we have a clearer description and consensus of extremism which can be used by the police, government and public bodies to help them carry out their roles.

“A clearer description will also help build a whole society response by providing a better understanding.”

Police chiefs have emphasised that Extinction Rebellion is not considered to be an extremist or a terror organisation, and they do not seek to stifle the legitimate right to protest.

But recurring examples of Prevent training sessions featuring XR and others have been met with anger from the targeted groups and there is now increased political pressure for the independent review of Prevent to investigate what happened.

The review, which was written into legislation that passed into law last year, was left rudderless when less than 12 months after the review was announced its chair, Lord Carlile, was forced to step down after a legal challenge was brought against his appointment over the question of his impartiality.

In a letter to the home secretary, Davey and his Liberal Democrat colleague, Christine Jardine, the spokesperson for home affairs, call for clarity over the review and demand that the inclusion of XR and other nonviolent groups in some Prevent training materials falls within its remit.

Davey and Jardine say: “We would be grateful if you could update us on the progress of the independent review of Prevent, especially in light of the Guardian’s revelation that Extinction Rebellion was listed by Counter Terrorism Policing South East as an ‘extreme ideology’ that should be reported under the programme.

“This case highlights exactly some of the concerns that the Liberal Democrats and others have about Prevent. Teachers, childcare providers, NHS workers and others have effectively been told by police that they are under a statutory duty to report people for protesting about the climate emergency.

“That is very alarming for its implications for freedom of expression and the right to protest, as well as for undermining crucial trust between children and their teachers, patients and their doctors, individuals and the police.”

The letter asks when the home secretary expects to appoint a suitable reviewer and begin the review and to ensure its terms of reference include the effect of Prevent on human rights, including freedom of expression, adding: “The recent revelation about Extinction Rebellion make clear how important that aspect is.”

The Home Office has been approached for comment.