Comedian Alan Davies has apologised to Lord McAlpine for naming him in relation to false allegations about abuse at a children's home.
The former Tory politician's legal team is in the process of suing everybody who wrongly linked him to allegations of historic child abuse.
The claims were sparked by a Newsnight report which did not name Lord McAlpine but referred to a senior Conservative from the Thatcher era, leading to his identification online.
Last week the BBC agreed to pay the peer £185,000 for wrongly implicating him in a paedophile ring that targeted children at the care home in Wrexham.
But Twitter users had already taken to the social network site to tweet or retweet the libellous allegations.
Tonight, Davies, star of BBC2's QI, told his 444,000-plus followers on Twitter: "I've just written to Lord McAlpine to apologise for retweeting his name in relation to false allegations following a BBC investigation."
Sally Bercow, the outspoken wife of Commons Speaker John Bercow, is another Twitter user who Lord McAlpine's lawyers are considering suing.
Mrs Bercow wrote on 4 November: "Why is Lord McAlpine trending? *innocent face*."
She has defended her tweet describing it as not libellous - "just foolish".
The peer's solicitor, Andrew Reid, has said action will be taken against "a lot of people" who linked the former politician's name with the unfounded allegations.
He has also previously confirmed that a "very long list" of Twitter users had been compiled which included Mrs Bercow and journalist George Monbiot, who has already apologised.
Lord McAlpine is also seeking damages from ITV.
The broadcaster sparked fury after This Morning presenter Phillip Schofield confronted the Prime Minister with a list of names of alleged abusers which he found on the internet and asked David Cameron if he would investigate them.
The peer's legal team have said they want more than the £185,000 paid by the BBC.
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