Coun Jack Scott brought an emergency motion to full council this week, following a meeting with health chiefs who said the profession was reaching breaking point.
He said: “GPs are at the beating heart of the NHS, quite literally with their finger on the pulse of our communities, but this Government has undermined them and added pressure upon pressure.
“Now we are seeing the consequences of this in Norfolk Park where our surgery is under threat.
“There’s a consultation on losing a state of the art building that is less than eight years old, in a community where health inequalities are already stark, where people already do not always access the health care that they deserve and need.
“The national GP shortage has made finding new partners in this practice almost impossible and sustained cuts across the public sector have piled pressure on GP surgeries.
“The reason we brought this notion is that the scandal of what’s happening in Norfolk Park could easily spread to other parts of our city.”
The Lib Dems said a lack of investment in buildings also caused problems.
Coun Steve Ayris said: “Many GP practices are still operating from converted housing or old substandard facilities and the maintenance needs of the primary care is largely unknown. There’s no consistent data collected on it.
“Unfit buildings are an inefficient use of resources and light, affect employee morale and impact on the quality and continuity of care for patients.
“Primary care struggles to make use of hundreds of millions of pounds in recruitment cash because practices have no room to accommodate new staff.”
Green councillor Alexi Dimond said there were more than 100,000 vacancies in the NHS, including tens of thousands of GP jobs.
“GPs have long been sounding the alarm, nationally and locally, about the crisis in primary care. They, along with all NHS staff, have worked tirelessly to treat more patients with fewer resources and fewer colleagues but this is not sustainable and is taking its toll.”