Council bosses say work is ongoing to help reduce the number of rough sleepers and street beggars in the city amid concerns about rising numbers.
The issue was raised at the latest meeting of the full council with leaders telling elected members “everyone’s working very hard to do what we can.”
Coun Sonia Gildert (Conservative) said rough-sleepers have been spotted regularly on the porch of Fishergate’s former BHS store.
She said: “I have every sympathy if they are genuinely homeless but they must be known to the authorities, so what is being done about it?
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“Fishergate is our largest street (in the city centre), do we really want our visitors to witness such a sight?”
Members of the ruling Labour cabinet pointed to the work being done by the city’s Foxton Centre.
Coun Matthew Brown said: “We’re doing what we can but we’re swimming against the tide to fight this.
“This is a multi-agency issue because the people who are on the streets tend to have a very difficult lifestyle.
“We’ve got to work across a lot of partners (and) we’re doing that. Every one of these people has a story. You’ve got to get to the heart of this situation and austerity isn’t helping.”
Coun Gildert added: “Please don’t think I don’t care (about the rough sleepers) I am in league with the charities. I’m speaking up for the people out there.”