The BBC is under pressure to hold an inquiry into how tapes of Russell Brand and Jonathan Ross making obscene phone calls to the actor Andrew Sachs were broadcast on Radio 2.

Millions of listeners heard the two presenters leaving sexually explicit messages on the actor’s answerphone claiming that Brand had had sex with his granddaughter. Brand and Ross, two of the corporation’s highest-paid stars, described in graphic detail an alleged encounter between Brand, 33, and Georgina, 23. They then sang bawdy songs about the event and joked that Sachs may kill himself.

Sachs, best known for playing the hapless Spanish waiter Manuel in the classic sitcom Fawlty Towers, was said to have been deeply upset by the lewd calls, which were broadcast during Brand’s Saturday night show on October 18. His agent has written a letter of complaint to the Controller of Radio 2, Lesley Douglas, calling for an apology and demanding to know how the decision to air the tapes was made.

It would not be the first time Brand has made false statements about his sexual conquests. He incurred the wrath of Rod Stewart after claiming at an awards ceremony that he had had “a little go” at his daughter, Kimberley. Brand admitted later that he had not had sex with her.

Since the messages to Sachs were aired, Brand has expressed regret. He told his listeners on Saturday: “I’d like to take this opportunity to issue a personal Russell Brand apology to Andrew Sachs, the great comic actor who played Manuel, for a message that Jonathan and I left on his answerphone. But it was quite funny. But, sometimes, you mustn’t swear on someone’s answerphone and that’s why I’d like to apologise personally.”Ross has not commented on the incident.

The offending segment began with the pair preparing to contact Sachs for an arranged telephone interview. Brand told his listeners: “In a minute we’re going to be talking to Andrew Sachs, Manuel actor. The elephant in the room is, what Andrew doesn’t know is, I’ve slept with his granddaughter.”

The host then called Sachs and left a message during which Ross, 47, shouted: “He f***** your granddaughter.” Ross also speculated that Brand had “enjoyed” Georgina on a swing. During another message Brand told Sachs: “I used a condom.” Later, the pair joked that Sachs could kill himself over the incident. Imagining a news bulletin, Brand said: “The main news again: Manuel, Andrew Sachs, hung himself today.”

A BBC spokesman said that the corporation was not aware of receiving a complaint from the actor, although two complaints about the show had been made.An Ofcom investigation could be ordered into a possible breach of the broadcasting code covering individual privacy and material that may cause harm and offence. Brand and Ross could also face a criminal prosecution for making abusive phone calls.

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