There have long been complaints about the levels of silt in the river and concerns it could add to the risk of flooding.
City councillors had asked whether funds from a new levy on developers for local infrastructure projects could be used to clear it.
But a new report says it will not cut the risk of flooding in the city and would be “prohibitively costly” – £400,000 for the stretch in the city council area alone. The river is now only used by a handful of businesses.
Coun Terry Keal, chairman of the environment and transport overview and scrutiny commission, which asked for the report, said he thought dredging was essential. “I am 58 and people of my age remember when the river was desilted and when they used to build ships at Beverley – they would find it very difficult to move anything from Beverley to the River Humber now.
“You look at Holland and they are constantly clearing out their watercourses. For us to manage the drainage systems within this area, we must keep it free of silt.
“The council has asked for a number of years to look at the removal of silt because it has started to build up in areas around the Arctic Corsair and towards the tidal barrier and it is looking unsightly as well as taking up an area which could accommodate water.
“If that silt was removed it would certainly ease the amount of flood risk in the area.”
The report says money from the new levy would be better spent on other defence works including “aqua greens” – areas which can be enclosed to channel water away from properties.