A motion going before Stevenage Borough Council calls for the change to help ease overcrowding.
A passenger says he has spent extra money on parking, fuel and taxis to cope with train disruption.
The line is blocked between London Kings Cross and Stevenage, LNER says.
Disruption on services between Ely and King's Lynn is expected to continue until 18:00 BST.
Travellers say the problems have made them late for work and miss hospital appointments
With soil shrinking in the heat, Network Rail says trains will be slower while engineers work.
It is because roof-mounted arms connecting trains to overhead electric wires are being checked.
Thameslink, Southern, Great Northern and Gatwick Express services will be nationalised on Sunday.
The incident has been referred by Hertfordshire Police to the Independent Office for Police Conduct.
