Headteachers have described the “sinister” intimidation tactics being used by protesters against the vaccination against Covid of teenagers in schools.

“It started with a few emails from a group calling itself Lawyers for Freedom,” the Guardian was told by the headteacher of one of a number of Liverpool schools that have come under pressure from anti-vaccine activists. “An email is relatively easy to ignore.”

The protests soon escalated, however, with “aggressive” leafleting of pupils by five or six protesters as they left school. The head dialled 999, but the police did not come.

“It felt disproportionate,” said the head. “We know there was at least one student who came back into school and was quite upset by what was going on.”

That was followed by a visit from a small group of protesters who gained access to the school, demanded to meet the head, then served quasi-legal documents warning that they would be held legally responsible if any child suffered death or harm from these “experimental vaccines”.

The same has happened at a number of Liverpool secondary schools. The encounters were typically filmed on a mobile phone then posted on the social media app Telegram by a group calling itself Liverpool’s People’s Resistance UK, naming schools and in some cases teachers, declaring, “Notice served.”

“It was pretty aggressive,” the head said. “They came up to reception asking to speak to the headteacher about a legal matter. They insist on reading from a script and they film the whole process on a mobile.

“Once they’ve handed the papers over, they tend to disappear. They’ve got the footage they want. It almost feels like it’s a trophy. There are Trumpian undertones to what these groups are doing. If they started describing themselves as patriots, I wouldn’t be surprised.”

The numbers of protesters involved is hard to pin down. An investigation by the Liverpool Post found that parents appeared to be contacting a group administrator called George to arrange for a visit and for papers to be served on their school. Having visited the school, they then boast about frightening teachers and at one point say about a headteacher: “She can’t run, she can’t hide.”

The head who spoke to the Guardian said he thought that some of the anger was from disenfranchised parents who were using the vaccine to pursue other grievances with their school. “To what extent the vaccine is a contributory factor, I don’t know,” he said. “What these sorts of groups are doing is saying, ‘We can do things. We can intimidate schools.’ It is sinister. Headship is a challenging enough vocation as it is. I fear what intimidation of this nature might do to future headship recruitment.”

A spokesperson for the Association of School and College Leaders agreed there were “sinister undertones” to what was happening in Liverpool, but they had not heard of this kind of organised activity elsewhere.

Elsewhere, anti-vaccine protesters have caused distress to pupils and staff while picketing school gates. Pupils at St Thomas More Catholic School in Blaydon, Gateshead, were distraught after anti-vaccine protesters showed them pictures of what appeared to be dead children.

Thames Valley police were investigating reports that a teacher was verbally abused by protesters at Beaconsfield School, one of a number of anti-vaccination protests at schools in Buckinghamshire. In Kent, police have been asked to lay on extra patrols after pupils were targeted by protesters.

A government spokesperson said: “It is never acceptable for anyone to pressurise or intimidate pupils, teachers or the wider school community, and protesters engaging in this type of behaviour should immediately bring it to an end. The police and local authorities have a range of powers available for managing protests at a local level and these can be used where appropriate.”

Supt Pete Steenhuis of Kent police said: “We respect that everyone has a right to peaceful protest and will balance these rights against the potential for disruption outside Kent and Medway schools.”

Paul Whiteman, general secretary of the National Association of Head Teachers, called for protesters to behave more responsibly. “Whatever your views on vaccination, it is never OK to make children feel scared and intimidated as they arrive at school.

“People have the right to express their concerns, but this must be done appropriately. Schools are not the place for angry protests. We would urge anti-vaccination campaigners to behave more responsibly and to carefully consider the impact their actions are having on children.”