Some school trips or sports tournaments rely on drier weather but have to be booked well in advance for the exemption, otherwise the £50 charge is passed on to schools.
Letters seen by the BBC, from schools which did not want to be named, told the council the five-day notice period was “not workable” and the school or coach provider would have additional costs.
Another said any additional costs only made it more difficult to continue to offer a range of activities.
Paul Harrison, of Central Travel in Sheffield, said many schools therefore were having to turn down “necessary” outings and swimming trips, and that the current system meant a member of bus staff spent around two hours a day filling out paperwork.
He said: “The impact is damaging the children, either them going swimming or on days out to animal parks. It’s impossible to work with.
“All it’s doing is working against the children in Sheffield. They’re the ones that are losing out.”
The council said since Sheffield’s CAZ was introduced in February 2023, data showed the number of the most polluting vehicles driving through the city centre has fallen by up to two thirds.
