Anti-vaccination protesters were reported to have gathered outside Madeley Academy during the school run.
A video posted on social media showed two protesters set up with a number of placards on the pavement and a bank near to the school on Thursday. It is believed to have been at least the second time the group has gathered.
The yellow placards had a number of slogans, including 'please don't jab our kids', and 'the media is the virus'.
Police have confirmed there had been no formal complaints over the issue and that no action has been taken against the protesters.
The UK Government recently announced plans to offer a Covid-19 vaccine to children in England and Wales aged 12 and over.
Councillor Shaun Davies, the leader of Telford & Wrekin Council, has now written to the region's police and crime commissioner urging him to press the government for fresh powers that would allow councils to stop people protesting outside schools.
He said: "Quite clearly I cannot see a set of circumstances where it is justified for people to be protesting outside a school.
"What we desperately need as a borough and as a country is for kids to get into school and make up for the time they have missed and to have a normal school life again.
"Having people outside to protest about one issue or another is simply not normal."
He added: "It is an unacceptable invasion of children's school life. Whatever your views are on this, it is not fair trying to influence an 11-year-old child."
A Telford & Wrekin Council spokesman said they had discussed the issue with the police.
He said: “We are aware that anti-vaccine protests have recently taken place outside schools in our borough and we are working closely to support the local police in handling them.
"Council Leader Shaun Davies has also written to the Police and Crime Commissioner to ask for councils to have powers to move people on, if necessary.
"The continuity of our children and young people’s education in a safe environment, without any hindrance, is a main priority for us.
"While we understand people’s rights to have a voice on Covid-19 vaccination, protesting outside schools should be avoided as it might cause distress and disrupt education."
"Ultimately, the decision to have or not the Covid-19 vaccination is up to the children and their families which should be respected.”
West Mercia Police declined to comment on the issue.