The Finsbury Health Centre in Islington, north London houses two GP practices, as well as dental services, podiatry, physiotherapy and the Michael Palin Centre for Stammering Children.
But Islington PCT says that it cannot afford to maintain the grade-I-listed building.
The health centre, which opened in 1938, costs £500,000 a year to maintain. Local Liberal Democrat parliamentary candidate Bridget Fox said the situation was 'ridiculous'.
'Local GPs have to make way for polyclinics, while existing polyclinics have to close,' she said.
Some services are being moved to Upper Holloway at the other end of the PCT, sparking off protests from locals.
The centre's two GP practices will transfer into a new purpose-built health centre next door, and will not be put out to tender, the PCT said.
A spokesman for Healthcare for London said that the building was not a polyclinic, because of its limited range of services and poor disability access.
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