Sgt. Jeremy Scott of the Metropolitan Police is understood to have published a number of offensive messages since Margaret Thatcher’s death.
He is said to have claimed her death was “87 years too late” and added that the world was a “better place”.
The Met described the comments as “completely unacceptable”.
After the tweets were widely reported Sgt. Jeremy Scott took the matter to the Directorate of Professional Standards.
The 52-year-old police officer then submitted his resignation before a police suspension over the incident came into force. It was accepted with immediate effect.
He had reportedly described news of the death as “marvellous stuff” and expressed a wish that the current prime minister, chancellor and home secretary were next.
Commander Allan Gibson said: “This officer’s behavior was completely unacceptable and it is right that he has resigned.”
On Thursday, British PM David Cameron branded some reaction to the death of Lady Thatcher as “pretty distasteful”.
David Cameron went on: “I think the overwhelming sense across the country – and you can see it yesterday in the House of Commons – is that we are mourning the loss of someone who gave a huge amount to this country, an extraordinary leader.”
Margaret Thatcher’s funeral is to be held in London on Wednesday, April 17.
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