Councillors in Bath hope to use government legislation in an attempt to reduce the number of lorries driving through the city.
At present the A36 Cleveland Bridge is designated as a primary national route.
Bath and North East Somerset Council says by removing the designation it can impose a weight limit on the bridge.
Conservative Councillor Bryan Chalker said the sooner it could ban lorries from passing through - rather than making deliveries - the better.
"This Grade II-listed [former] toll bridge was designed for horse and carriage and strengthened in 1930 to allow 38 tonne lorries," he said.
"Now we are up to 44 tonnes and increasing. It's only a matter of time before this delightful old bridge shakes its self to pieces.
"We have to do something. We are a World Heritage site and not a through route.
"We cannot take any more heavy vehicles coming through."
Under the Transport Select Committee study into the major road network de-trunking would allow the transfer of trunk roads from the Highways Agency to allow local authorities to integrate roads important to the local area into their own transport plans.
To de-trunk a route local authorities have to apply to the Department for Transport.
However if the road is deemed of "national importance" then the transfer would not take place.