Alford, 25, who plays fireman Billy Ray, was told by London Weekend Television to stay away from today's filming - the last day scheduled for production of the programme.
LWT's statement yesterday read: "Following serious allegations in last Sunday's News of the World, LWT has taken the decision to suspend John Alford from London's Burning.
"He has already completed the majority of his filming for the current series but will not complete the single day's shooting this Saturday that was outstanding. That is all we can say at this stage."
Alford's contract expires next month and it is unlikely to be renewed.
The Glaswegian actor was exposed by the Sunday newspaper's chief investigative reporter, Mazher Mahmood, in an undercover operation.
Alford was photographed allegedly trying to sell cocaine to the reporter and bragging about how pure his supplies were. It was reported that he sold three wraps of cocaine and cannabis resin for pounds 300 to the journalist.
Alford reportedly said "he could get away with it" because he was a celebrity.
In a taped conversation, the paper also claims Alford said he could not live without cannabis. During the last three years, the popular actor has seen his salary jump from pounds 7,000 to pounds 50,000. But the drug link allegations could spell the end of his acting career.
He began acting at the age of nine and he played a leading role in the school drama, Grange Hill.
The day after publication of the story, it was reported that the actor from Hadley Wood, north London, had been told that despite the allegations his job on the popular soap was safe.
However following a further grilling by London Weekend Television executives, the decision was made to suspend him.
The News of the World has handed its material to the police, it said yesterday.
Stuart Kuttner, the newspaper's managing editor, said: "The police have asked us for all our evidence and we are co-operating fully."Alford's agency declined to comment on the allegations of drug taking and the actor's suspension from the programme.
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