The experimental traffic regulation has been in force since Monday and has proved unpopular so far with cafes, restaurants and town centre residents.
From Monday, buses and taxis have been allowed up Wyle Cop and along the High Street and Shoplatch, after daytime closures to all traffic were previously in place for social distancing purposes.
But cars and delivery vehicles have been ignoring signs ordering them to not use the route.
Meanwhile, adding to the disappointment of hospitality firms, a number of cafes, bars and restaurants have also been ordered to take their tables off the streets.
When the experimental new measures were revealed last week, Shropshire Council's deputy leader Steve Charmley said the new measures would give hospitality businesses the chance to "embrace cafe culture".
But cafe owner Gwen Burgess is not impressed with how the system is working.
She said: "If the road is open for buses and cabs, then all the other traffic will come through as well.
"And all the bus stops on High Street, Shoplatch and Barker Street are closed, which doesn’t really help passengers to access town. So, what we have now is – buses and cabs through, lots of other traffic through – but no bus stops or outside tables and chairs for all the hospitality businesses.
"It's not really very welcoming for visitors. It wasn’t really thought through very well."
Town Walls residents are also feeling fed up with the traffic situation, saying that allowing buses and taxis up Wyle Cop during the day is not doing enough to keep vehicles away for the medieval walls.
Residents will be speaking to the council tonight at a working group to discuss how the measures are working so far.
Andrew Bannerman, a resident in the area and former councillor, said: "There is a lot of frustration among residents. The changes that have been made are not helping.
"There have been three accidents recently on the narrow part of the road outside the cathedral, and you see people speeding to get through the traffic lights.
"Measures need to be brought in to slow every vehicle down and remove the traffic by at least half."
The experimental traffic order is in place until October.
Shropshire Council has been approached for a comment.