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Increased patrols outside schools have been demanded after groups of pupils were approached by anti-vaccination protesters.
Pupils were targeted by individuals in Gravesend on their way to and from school as a councillor says levels of intimidation have been unacceptable.
County councillor Jordan Meade (Con), who represents the Gravesend East Division at KCC, said: "Whilst I fully respect the right of an individual to protest, no child should be approached by strangers as they leave the school gates.
"Parents have been in touch to state how upset and scared their children have been and frankly I find the intimidation of pupils to be unforgivable.
"I have been in liaison today with local head teachers, and I am appalled that both staff and students have been made to feel vulnerable.
"I have requested that Kent Police put in operational patrols outside of secondary schools to provide some much-needed re-assurance to staff and students."
Over the past week protesters have been spotted outside Gravesend secondary schools including Thamesview, St George's Church of England School and Northfleet School for Girls.
Cllr Meade is asking groups to move away from schools and protest in a way that does not intimidate children.
The protesters have been standing outside holding yellow signs and handing out information leaflets to pupils about why they should not take up the Covid vaccine.
He added: "The protesters should ask themselves if they would be happy with strangers coming up to their children as they leave school.
"Parental consent is being requested before any child aged 12 to 15 is given the Covid-19 vaccination – in line with NHS rules – and the fact that these protesters think they know better than the parents concerned is simply abhorrent.
"The mental health of young people has suffered tremendously throughout the pandemic, and I am disturbed that we now have adults who are actively contributing to their anxiety."
Concerned parents are using Facebook to discuss the matter saying it is "intimidating" and their children are feeling "uncomfortable".
Police have not commented on whether patrols would be stepped up in light of recent events or Cllr Meade's request but a senior officer said schools have been advised how to deal with protests.
Supt Pete Steenhuis said: "We respect that everyone has a right to peaceful protest and will balance these rights against the potential for disruption outside of Kent and Medway schools.
"We have contacted all the county’s schools following the government’s plans to offer the vaccines to children and have provided advice that could help schools manage or defuse potential situations.
"Very often a simple request to peaceful protesters, asking them to stand next to school gates instead of in front of them, can de-escalate tensions.
"However, where a crime is committed or life is in danger, or where there is serious disorder or disruption to the public, Kent Police should be contacted by calling 999."
The schools were approached for comment.