Its commissioner Andy Lord has told the Standard that the issue could stretch to other lines as well and take years to put right.
Transport for London has said alternative journey plans can be made with London Buses, London Overground, Elizabeth line, Chiltern Railways, Great Western Railway and Greater Anglia all accepting London Underground tickets.
But why has the service been so poor on the network? Find out below – and also see the Standard’s live travel blog for the latest on the situation.
Why are there always delays on the Central line?
The line is suffering a chronic shortage of trains and it has been operating at times with barely half of the 78 trains required to run a peak service.
Mr Khan said: “Can I apologise [to] all those who have been struggling with the Central line in recent days.
“I will make sure that TfL colleagues let Central line passengers know the progress of improvements in relation to some of the challenges that have been faced in recent days.”
The trains have been out of action because the aging motors on the trains, which date to 1992, are suffering catastrophic failures and have to be taken out of service to be replaced.
Lord has admitted the shortage of trains could spread to other lines, such as the Bakerloo, Northern and Piccadilly, prior to its new trains arriving from 2025.
This is due to a lack of funding to carry out regular “heavy overhauls” over the past few years.
When will the problem be sorted?
As Ross Lydall has reported, Transport for London has said some of its motor parts have been refurbished and that repairs have been “progressing well”.
It added that some trains could re-enter service in the weeks to come but that will not be the end of the saga.
A TfL statement added: “While this should help improve the service, the motor failures are still occurring at a higher rate than we’ve experienced before and some disruption to normal service levels is likely to continue for some months.”
The Central line fleet is undergoing a £500m modernisation that aims to keep the trains running for another 10 to 15 years.
TfL cannot afford to replace the fleet at the same time as replacing the Piccadilly line trains, which is costing £1.6bn.
Five Central line trains at a time are taken out of service for 10 weeks and rebuilt at a new depot in Acton. The refurbished trains then have to be tested – delaying their full reintroduction.
Transport for London’s chief operating officer Glynn Barton said: “We are working round the clock to get as many trains out there. What we will be doing is making sure we have a regular service for customers – a service where they know what to expect when they turn up.”