The extension at the centre, which has a pharmacy and an opticians, would have had consultant rooms and a medical theatre.
The scheme would also have included new ductwork, a raised flatroof and gable, and a two-metre (6.5-ft) high fence.
In its statement, the neighbourhood council added: “It is surprising that the current application has not referred to the obvious car parking problems.
“There has been no attempt to address this problem, to alleviate any concerns nor to make any reference to Werrington Neighbourhood Plan.
It said the planning application must not be considered until “the applicant has successfully acknowledged and addressed this problem”.
The local highways authority was also worried about parking.
It said the centre did not have “sufficient” parking, which had “resulted in unsafe parking practices and an increase in on-street parking along Church Street”.
There were also objections from the city council’s drainage officer and tree officer.