Blood testing at a troubled new £13m health centre could return in March.
The service was withdrawn from the Jubilee Health Centre in Wallington last month following concerns about fire and water safety.
Tom Brake, MP for Cashalton and Wallington, said it was "embarrassing" that the service had to be removed and demanded a quick resolution to the problems.
He said: "The situation with Jubilee is unacceptable – £13 million facilities built in the middle of Wallington to improve accessibility, and patients still have to travel to the local hospital for basic services."
"I have received many complaints from local residents about this. I am very happy to see we are finally getting somewhere and that the issue is now closer to being resolved."
Mr Brake vowed to monitor the situation.
Health organisations have pledged to work with the landlord to address all the critical issues by 26 February and subject to this, the blood testing service could be reintroduced by March 4.
Six-time Paralympic gold medallist and wheelchair-bound Wallington resident David Weir officially opened the centre in October last year.
At the opening in May, former mayor Dr Brendan Hudson hailed it as a "great day for the NHS", but since then the centre has been blighted with problems.
In its opening month, some patients, who had booked appointments weeks in advance, were turned away by a security guard due to "last-minute contractual issues", with one patient being taken to hospital.
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