Parents of hundreds of pupils decanted last year to the former Lairdsland School in Kirkintilloch fear for their safety as a result of work on the shared space.
Members of Holy Family Parent Council are demanding East Dunbartonshire Council demonstrate its commitment to keeping their children safe at the Kerr Street school.
They are also angry at the lack of notice and consultation about the first phase of the works which began on Monday, February 8.
Cowgate is now closed to vehicles between Townhead Bridge and Catherine Street for three months.
Buses and vehicles can use Kerr Street and Catherine Street and there is a diversion from Townhead onto New Lairdsland Road.
A parent committee member posted on the group’s Facebook site: “As your Parent Council, we share your frustration in the short notice of this announcement and the unknown impact it will have on the access and safety of the area surrounding the Kerr Street site during the works.
“We will not let this matter go and will continue to seek clarity from the council and ensure their commitment to the safety of our children and the return to the fully refurbished Boghead Road site in a timely manner.”