LONDON—A British politician wrongly accused of child sex abuse has dropped his threat to sue people who named him on Twitter—as long as they have fewer than 500 followers.

Alistair McAlpine is asking those tweeters with fewer than 500 followers who falsely labeled him a pedophile to donate 25 pounds ($38) to a children's charity.

McAlpine has already received damages from the BBC, which ran a report last year linking him to decades-old child sex abuse.

The BBC report did not name McAlpine, a member of the House of Lords, but it led to widespread Internet chatter about him.

McAlpine said Thursday he would proceed with a lawsuit against Sally Bercow, wife of the British Parliament speaker, who named him on Twitter, where she had thousands of followers.