GPs from Woodlands Surgery, in Sidcup, took over the practice in Longmead Drive 18 months ago, when its previous occupant retired. But he recently told the practice he would not be renewing its lease, because he planned to sell the building.
Neither Woodlands Surgery nor Bexley Care Trust can afford the asking price.
Longmead Drive's GPs are transferring to the practice's other premises on Halfway Street, which is two bus rides away. The practice's 2,500 patients have been told they can go with them, or register with other local GPs.
But Ross Downing, who represents the area on Bexley Council for the Conservatives, said one of the alternative practices was refusing to take new patients, and none was accessible by public transport.
'The practice has a high percentage of elderly patients, and it's in quite a deprived area,' she said. 'To get to Halfway Street isn't a possibility.'
She added that the closure clashed with the 'Picture of Health' consultation on health services in south-east London. 'If you look at that, every page mentions services closer to home,' she said.
The surgery will close its doors on 31 March. More than 400 local residents have signed a petition demanding it stay open.
Comment below and tell us what you think