LONDON (Reuters) - Britons who posted remarks on Twitter and in blogs wrongly identifying a senior Conservative politician as a child sex abuser might face prosecution after police said on Wednesday they were looking to see if any crimes had been committed.

Lord Alistair McAlpine, an ally of former Prime Minister Margaret Thatcher, was widely named on social media sites as being the unidentified politician accused in a report by the BBC's Newsnight program of abusing boys in social care.

McAlpine, who is 70 and in poor health, vigorously denied the claims and the abuse victim central to the BBC story later confirmed that the peer was not one of his attackers.

London's Metropolitan Police said no criminal allegations had yet been made but that detectives would be meeting with McAlpine to begin assessing whether action should be taken.

Under the Malicious Communications Act, people can be prosecuted for sending any electronic communication or article which conveys a grossly offensive message or information which is false and believed to be false by the sender.

"It is far too early to say whether any criminal investigation will follow," the police said in a statement.

The intervention comes as lawyers for McAlpine continued legal action against those who "sullied" his reputation.

The BBC has already agreed to pay 185,000 pounds ($294,400)over the Newsnight report, and his lawyers have also contacted ITV after a presenter on a chat show brandished a list of alleged abusers during an interview with Prime Minister David Cameron.

McAlpine has also threatened to go after Twitter users, and media reports said his legal team had identified up to 10,000 defamatory tweets.

Sally Bercow, flamboyant wife of Britain's parliamentary speaker, the man who keeps lawmakers in order during debates, is one of those who could face legal action.

Other Twitter users have been asked to come forward, apologize and make a "sensible and modest" donation to charity as compensation, at a level yet to be decided.

"Given the large amount of information that continues to be disseminated, the band for which the charity payment will be settled shall be when Lord McAlpine has a full understanding of this material," his lawyers said in a statement.

"The donation is intended for tweeters with fewer than 500 followers, but those with larger numbers of followers are still encouraged to identify themselves and offer their formal apologies at this stage."

(Reporting by Michael Holden; editing by Steve Addison)