A new surgery is needed in a rapidly expanding suburb in addition to an existing site being expanded, council chiefs have said.
It is hoped that Aslake Close surgery, Sprowston, will be refurbished and extended after the government approved the business case for capital funding in September this year.
The bold £25m plan includes four proposed primary care hubs in Rackheath, Sprowston, King’s Lynn and Thetford.
The first two are refurbishments of existing buildings and the latter two are new builds, according to an NHS Norfolk and Waveney spokesman.
Natasha Harpley, Labour councillor for Sprowston Central on Broadland District Council, said: "You have to improve services because surgeries are struggling due to the increasing number of houses being built.
"People are not getting appointments and are ending up in accident and emergency. Things are getting out of hand."
She added that infrastructure like surgeries need to be put in on new housing estates, instead of expanding the remit of current sites.
She said: "Everything is backwards and about playing catch-up.
"In an ideal world if you build new homes you should build a new surgery near them. It is common sense."
But she added she welcomed the surgery extension because "any improvement was better for patients".
Bill Couzens, Labour Sprowston Town Council chairman, said: "The issue for all surgeries, not just Aslake Close, is they are suffering from a lack of doctors."
He added the NHS needed to make sure it had "the right component of doctors" if the extension to Asklake Close - part of the East Norwich Medical Partnership - was built.
Mr Couzens said: "We would welcome more doctors and dentists. If the NHS wants more space we have got lots of areas in Sprowston that would be better to have an additional surgery.
"There are 1,500 houses being built behind Tesco and 1,500 homes in Salhouse Road. We need a surgery near where people live. The last thing you want when you are ill is travelling far."
In October last year, the NHS Norfolk and Waveney Clinical Commissioning Group (CCG) held talks over how to expand capacity at Sprowston Primary Care Centre in Aslake Close.
NHS Norfolk and Waveney was approached for further comment.
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