The Strictly Come Dancing announcer made the shocking allegations in a recording which was obtained by The Sun.
On the tape, Alan, 60, as asked how many people at the broadcasting company bought drugs at work.
“Erm, at least 50 per cent,” he said. “[the delivery man] just goes from desk to desk.
“The police can do nothing about the fact that he’s delivering desk to desk.”
When pressed further and asked if drug use is ‘rife’ at the BBC, Alan responded: “You say rife like it’s horrible and wrong.
“He only comes in because it stops him being intercepted by the police.”
But Alan has since denied his own allegations, insisting he was lying on the tape.
In a statement he said: “There is no truth to what I said. I was foolishly embellishing upon rumours I was aware of dating (back) from 20 or 30 years ago in relation to the commercial radio sector.
“I have no personal knowledge of these matters and have absolutely no reason to believe that the activities referred to in the edited extract of this covertly-recorded conversation take place or have ever taken place at the BBC.”