Rail union bosses met London Underground (LU) officials on Friday in a continuing row over safety.
Northern Line passengers are being advised to take alternative routes
Emergency braking systems on Northern Line trains have failed, so LU has introduced daily safety checks and is putting an extra driver in each train.
It means there is a reduced service leading to severe delays. On Friday evening there were just 51 out of 91 trains running.
Roger Evans, Tory London Assembly member, said it "beggars belief".
A spokesman for rail union RMT said drivers were exercising their legal right not to move trains if their safety is at risk.
'Get a grip'
He said the emergency braking system, designed to stop trains going through danger signals, had failed four times in as many weeks.
Roger Evans, chairman of the London Assembly Transport Committee, said : "This latest news on braking systems beggars belief considering the money that's being poured into the Underground system.
"Ken Livingstone (London Mayor) and Bob Kiley (London's Transport Commissioner) really have got to get a grip on London Underground and sort out these basic problems before the entire system grinds to a halt."
Under the Public Private Partnership (PPP) scheme, Tube Lines and Alstom are responsible for maintenance on the Northern Line.
A spokesman for LU said it had been pressing both firms to resolve the situation for several weeks and was now directing and overseeing the work of Tube Lines and Alstom.
"The fact that they have not resolved the situation is completely unacceptable," he said.
A spokesman for Tube Lines said its top priority was passengers' safety and every train was being checked before going into service.
He added that Alstom's performance had not been good enough and Tube Lines would not rule anything out to resolve the situation, including terminating the contract.
Alstom would not comment on its contract, but said it had been working closely with LU and Tube Lines.
The cause of the faulty brakes has still not been established.
Northern Line passengers are being advised to take alternative routes while delays continue.