Heather told Sir Paul that she was not responsible for the recording and that the tape was handed to her by a third party.
The existence of the tape will cause enormous embarrassment for Sir Paul. The 64-year-old former Beatle has maintained that there was never any rift between Heather and his children, despite rumours to the contrary.
Sources say he is 'appalled' that the conversation was bugged and an investigation has begun. Sir Paul and his aides are also deciding whether to report the matter to police.