Carol Thatcher, the daughter of the former Prime Minister Margaret Thatcher, is facing a possible ban from the BBC after referring to a tennis player as “a golliwog”.

The BBC told The Times last night that it had held urgent talks with Thatcher, 55, and was seeking a formal apology before it agreed to allow her to reappear on the network as either a contributor or presenter.

The incident occurred on Thursday night after The One Show when Thatcher, a roving reporter on the programme, was in the green room with its presenter, Adrian Chiles, and other members of the production team.

During a conversation about the Australian Open tennis tournament Thatcher used the word “golliwog” in what is understood to have been a reference to a player in the men’s competition.

A BBC insider said that Chiles, who also presents sports programmes, was “very shocked” by the remark and that others in the room told Thatcher that they considered her language offensive.

But friends of the journalist and author said that the remarks were made jokingly during a private conversation that took place after several drinks in the green room. They said that there had been no complaint at the time and that Thatcher only became aware of having caused potential offence 48 hours later when the BBC contacted her agent.

A BBC spokesman said: “The BBC considers any language of a racist nature wholly unacceptable. We have raised the issue with the individual concerned and are discussing it as a matter of urgency.”

Sources at the BBC said that Thatcher would be “in a difficult area” with regard to future appearances unless she was prepared to make a formal apology for the remark.

The website for The One Show carries a profile of Thatcher that states: “No story’s too big or too small for Carol.”

It describes her as having a “dry, self-deprecating wit and tenacious spirit” and boasts that “she always brings her inimitable style” to the programme.

A spokesman for Thatcher, who has been a regular contributor to The One Show for three years, said that the comment had been “an off-the-cuff remark made in jest”.

Her spokesman added: “Carol never intended any racist comment. She made a light aside about this tennis player and his similarity to the golliwog on the jampot when she was growing up. There’s no way, obviously, that she would condone any racist comment – we would refute that entirely. It would not be in her nature to do anything like that.”

Thatcher had apologised to the programme’s producer for any offence but was said to be “mortified” that the content of an off-air conversation had been disclosed by a BBC employee. Her spokesman added: “This was a conversation between Adrian and Carol in the green room and the comment was meant as a joke. It is disgusting that we’ve had a leak of private conversations in the green room – the BBC has more leaks than Thames Water.

“Carol is mortified that anyone should take offence at a silly joke. She has summarily apologised.”

Thatcher attracted criticism last year when she revealed in a memoir that her mother had been suffering with dementia for several years. She wrote of the former Conservative Prime Minister: “Watching her struggle with her words and her memory, I couldn’t believe it. I had always thought of her as ageless, timeless and 100 per cent cast-iron damage-proof. The contrast was all the more striking because she’d always had a memory like a website.”

Neither the BBC nor representatives of Chiles and Thatcher were prepared to name the tennis player who was under discussion. Her friends said that she had been referring to the player’s hairstyle and was not making a racist comment.

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