Delays on the Piccadilly Line could last until February, the RMT Union has claimed.
Passengers have been plagued by delays on the line because some trains have been taken out of service in order for the wheels to be repaired.
RMT believe the delays will continue through to February next year, adding that it "doesn't make sense" that the Night Tube should launch on Friday (December 16).
A RMT spokesman said: "Our position remains the same.
"You have only got to look at the daily situation on the Piccadilly line and the current availability of trains.
"We have been told that the situation is going to go on until February.
"It doesn’t make any sense when the daily service is currently a skeleton service to start running the Night Tube on the line.
"We think the Night Tube operation should be suspended until the fleet problems have been resolved."
Transport for London (TfL) has dismissed the claims, adding it now has 66 trains in operation from the total of 79 needed for full operation.
A spokesman said: "I have no idea where that is coming from (RMT claims), I don't know who has told them that.
"We are working hard to get the trains back on the service.
"We're talking more in weeks."
The spokesman added that the Night Tube will definitely go ahead on Friday.
Yesterday (Tuesday December 13) A London Underground source told getwestlondon: "At the moment, the Night Tube will be going ahead.
"We're not entirely sure yet as to how the timetable will work, we have improvements on the line each day.
"We can't say for sure but as it stands, it's still launching as expected."
London Underground said the wheels of trains were damaged by wet leaves which left them with no choice other than to pull half the fleet in order to repair them.
The problem has been ongoing since November.
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