Councillors want more control over licensing to tackle the issue of shops selling cheap alcohol.
Members of Leeds City Council's health scrutiny board said the Government should look at giving more powers to the council over the refusal of booze licences.
The call came as councillors discussed a new report - exclusively revealed in the Yorkshire Evening Post last week - which said alcohol-related harm cost Leeds 438m in just one year.
Coun Jamie Matthews (Lib Dem, Headingley) said: "Where we fall down is the licensing policy, which seems to work in relation to pubs but it does not seem to work when it comes to the sale of alcohol in supermarkets. If you open a 24-hour alcohol-selling supermarket in a student area, it's going to cause all sorts of problems in terms of alcohol consumption.
"This is putting increasing strain on our services and we need some sort of recognition that we cannot go on granting longer and later alcohol licences."
Coun Suzi Armitage, chairman of the city council's licensing committee, said it was a "major problem" that they could refuse a licence for a pub but it was more difficult to do the same for a shop.
Coun Armitage (Lab, Cross Gates and Whinmoor) said Government intervention was needed.
Health board chairman Coun Mark Dobson (Lab, Garforth and Swillington), also a member of the licensing committee, added: "Sometimes we are passing something but it's through gritted teeth. We know it's not a good decision but we feel the objectives of the Licensing Act have been ticked so we feel somewhat hamstrung."
Dr Ian Cameron, NHS Leeds and Leeds City Council director of public health, said licensing officers were part of the group developing the city's new alcohol action plan and they were keep tabs on changes to the Licensing Act.
Dr Cameron also praised the Yorkshire Evening Post's series of articles which he said were "excellent" and brought to life the issues.
He added there was no magic bullet to solve the problem of excess drinking: "What we have got to do overall is change social norms towards alcohol."