The roadworks are part of the construction of a new railway station, being delivered by Transport for West Midlands (TfWM).
Further up the road from the supermarket, a family-run florist and funeral business said it had also been impacted by the work.
Joe Evans, from Jennifer Ashe & Son, said: “Seeing as the road is now a one-way system, it means people aren’t paying attention to the businesses that we have, and the items that are on offer outside.
“The florist has been severely affected and the profitability is down month on month from what we’re expecting in sales.”
Work for the station is taking place on Bilston Street and New Road.
But at the same time, work is also taking place on Noose Lane, Pinson Road and Rose Hill for a new cycle scheme.
At rush hour, the traders say, parts of the town are experiencing slow traffic for long periods.
“Being a funeral directors, as you can imagine we have cars arriving and departing the branch at all times of the day, so this is severely affecting the funeral times,” Mr Evans said.
“So we are having to make adjustments to cater for the fact that sometimes there is a standstill traffic queue outside our premises.”
