PARIS — The Internet, it is sometimes said, turns every citizen into a journalist. If that is the case, some Twitter users in Britain are discovering one of the downsides of the business.

As many as 10,000 Twitter users reportedly face the threat of legal action because of comments posted on the Internet or forwarded to others in which they referred to a BBC report wrongly linking a former Conservative Party official to the sexual abuse of a child. The official, Alistair McAlpine, was not named in the Nov. 2 BBC report, but enough clues were provided that Twitter users were able to identify him — which they did, in great numbers.

The BBC quickly settled a libel claim, paying Mr. McAlpine £185,000, or nearly $300,000, and apologized for the error as a case of mistaken identity. Another British television broadcaster, ITV, agreed on Thursday to pay Mr. McAlpine £125,000 to settle another claim, this one over a subsequent broadcast in which a list purporting to show Conservative figures linked to sex abuse accusations had been visible to viewers.

Mr. McAlpine did not stop with the mainstream media. On Friday, a spokeswoman for the politician told The Guardian newspaper that his lawyers had identified 20 “high-profile tweeters” from whom they were seeking libel damages. Among them were a comedian, Alan Davies; Sally Bercow, the wife of John Bercow, the speaker of the House of Commons; and George Monbiot, a Guardian columnist.