Although Churchill wrote his own speeches and delivered them in the House of Commons himself, the recordings broadcast to the world over the radio were performed by actor Norman Shelley doing doing a Churchill impersonation.
The man himself was, understandably, far too busy with more important matters to sit in a radio studio and read off a speech he had already delivered once.
Irving wasn't the only one who said that. He was just the only one to use it as a mark against Churchill.
Churchill was a busy man. The House of Commons wasn't set up to record his speeches. Shelley could do a dead-on impersonation of the man. While the government and Churchill fanatics continue to deny it, people who were with the BBC and friends of Shelley have said the rumors were true.
I don't think it detracts from Churchill or diminishes the power of his speeches in any way. All nations did stuff like this at the time. Americans used to film fake combat with actors portraying soldiers on both sides then show it in newsreels as authentic combat footage.