Others said the area is often used for drug use and that human faeces have had to be cleared by local business workers.
Council officers said they want to “break the cycle” of anti-social behaviour and that they have had “significant pressure” from local firms to tackle the issue.
Plans were approved despite just 31 responses to a public consultation.
Scrutiny chair, Councillor Chris Burke, described the passage as “not the city at its most glorious”.
“It is definitely an attraction for some people,” he said.
“But it is not something that you would want tourists to see.”
Policy Scrutiny chair, Councillor Chris Burke.
Councillor Tom Dyer said he supported the plan, but added that something needs to be in place to protect people in case the problem “disperses”.
“It’s no secret that this passageway needs to be closed,” he said.
“We do not want any harm to be done to tourists, people of this city or people who go down the passage.
“But the last thing that we want is to close this and the problem disperses all over.”
The committee asked for further analysis to be done on how to protect the public should anti-social behaviour spread to other passages in the city.
Problems have been highlighted over the last year relating to drug use and discarded paraphernalia at St Peter’s Passage, which is also being used as a toilet with strong smells of urine.
The passageway was previously earmarked for closure back in 2015 until the plan was dropped by the city council due to a low consultation response.
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