Part of the town centre – the High Street and Shoplatch – is closed to traffic between 11am and 4pm every day.
The move is as part of Shropshire Council's move to provide more outdoor space for visitors to Shrewsbury and help with social distancing.
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The delay by the Government of unlocking the final coronavirus restrictions until July led the council to extend the closure into next month.
But the decision has been met with dismay by many people who say the traffic is just been pushed onto the narrow Town Walls street. And they are worried that the system may continue past Covid.
Former councillor Andrew Bannerman said: "The simple fact is that when prevented from ascending Wyle Cop, the traffic simply migrates to Town Walls.
"There are temporary notices suggesting through traffic should use the inner bypass, but observation suggests these are heeded by few drivers.
"The result has been a huge increase of traffic on Town Walls, a narrow, historic street, which cannot sustain this," he said.
Mr Bannerman highlighted the amount of pedestrians who use or cross the road.
"Many students walk along Town Walls and cross it daily and large numbers cross it to reach The Quarry. They, along with residents, visitors and church congregations have had to put up with a surge in pollution, noise and vibration," he said.
"Many drivers use adjacent streets, especially St John’s Hill, as a cut-through to Barker Street and the west and north of the town, endangering pedestrians. They also use the newly-surfaced, 'pedestrian-friendly' area by the market."
Mr Bannerman said the situation was so bad last year that residents organised surveys which showed that traffic exceeded 600 vehicles per hour several times in a day.
He added: "Very large vehicles threaten the stability of the historic fabric – gas mains have ruptured and stone eroded. A working group including residents’ representatives, along with council officers and the BID, is trying to reach a solution, but the council has not yet installed a system which adequately protects Town Walls and adjacent streets. "
Councillor Steve Charmley, Shropshire Council's cabinet member with responsibility for highways, said: “It’s important to continue with current arrangements which allowed greater use of outside space for social distancing.
“With infection numbers on the rise, it is vital that we all continue to adhere to social distancing rules, which is why the traffic interventions in Shrewsbury town centre were originally introduced.
“We are certainly not intending to go back to square one whenever restrictions are removed, as it’s clear there is support for keeping the town centre free of through-traffic.
"However, we are also aware that increased traffic on Town Walls has created difficulties for residents, so we are considering how to minimise that by managing bus routes and re-routing through traffic."