Police have told teachers that they should consider envir­onmental activists and anti-fracking protesters as potential extremists under the government’s Prevent counter-terrorism strategy, TES has learned.

More than 100 teachers from several schools were given the advice during a Prevent training session in West Yorkshire, where they were also warned by a police officer about extreme anti-capitalist groups.

One teacher said the officer went on to refer to the behaviour of Green Party MP Caroline Lucas – who was arrested for her part in blocking a road at an anti-fracking demonstration in 2013 – as an example of extremism.

Teaching unions have condemned the advice. Ms Lucas has told TES that she is “shocked” and is planning to write to the police to complain.

“Equating peaceful political demonstrations with violent extremism is both offensive and deeply misguided,” the MP said. “It’s this kind of thinking that has led police in this country to waste vast amounts of taxpayers’ money in infiltrating environmental groups.”

The latest version of the Prevent strategy was published in 2011 and lists international terrorism (including al-Qaeda), as well as terrorism connected with Northern Ireland and the extreme Right, as threats. No mention is made of environmental or anti-capitalist groups.

Amanda Brown, assistant general secretary of the NUT teaching union, said: “I’m quite alarmed that a police officer, who people would trust and think is offering the right advice, would say that it might be considered as extremism that someone is expressing their right, in a democracy, to express a view.”

Sources at West Yorkshire Police have confirmed that an officer speaking at the teacher-training session on extremism, delivered in Holmfirth last term, had referred to the arrest of an MP on an anti-fracking demonstration as an example.

They said the officer chose to refer to anti-fracking demonstrations during the session because the protests had been in the news. He had not intended to suggest that the arrested MP was a violent extremist, merely that demonstrators faced a risk of arrest.

The sources also confirmed that the attending teachers, drawn from across the Kirklees district, were warned about anti-capitalist and environmental extremists, as well as far-Right and al-Qaeda-inspired extremism.

The government has defined extremism in its Prevent strategy as: “Vocal or active opposition to fundamental British values, including democracy, the rule of law, individual liberty, and mutual respect and tolerance of different faiths and beliefs.”

But Dylan Murphy, a history teacher present at the training day, said he understood the police officer to be saying something different. “The thing that set alarm bells ringing in my head was when he started talking about environmental activists,” he said. “I thought, ‘Are you equating anti-fracking protests and environmental protesters with neo-Nazis and terrorists?’ ”

Mr Murphy said the officer had also mentioned the arrest of Ms Lucas.

Russ Foster, assistant chief commissioner at West Yorkshire Police, said: “The police acknowledge the right of people to protest in a lawful manner. However, should an individual seek to use violence in furtherance of their view, then Prevent would seek to engage with them. Prevent is not a criminal sanction. It is the partnership response to individuals who are at risk of being drawn into violent extremism, with the intention of preventing them coming to serious harm or causing serious harm to another person.”

Mary Bousted, general secretary of the ATL teaching union, said: “This is obviously a training session where the presenter didn’t follow his lesson plan properly, and was drawn into a very vague and ill-defined discussion of various forms of extremism, which he didn’t handle very well.”