The Metropolitan Police said the three constables were arrested in December on suspicion of involvement in "possession and distribution of obscene images".
The officers are from the Diplomatic Protection Group (DPG), which guards foreign embassies as well as other sensitive government buildings.
"On December, 19, 2013, officers from the Directorate of Professional Standards arrested three police constables from the DPG on suspicion of being involved in the possession and distribution of obscene images via mobile phones. This is contrary to both the Obscene Publications Act 1959 and also the Criminal Justice and Immigration Act 2008," a Police spokesperson said.
The officers' homes had been raided and searched and one officer was suspended from duty while two others remain at work but on restricted duties.
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The Met said it had "voluntarily referred the matter" to the Independent Police Complaints Commission, which had said it should be "investigated locally" by professional standards officers.
A file has been passed to the Crown Prosecution Service (CPS) and the professional standards misconduct investigation is on hold pending a CPS decision.
According to 'The Times', officers from Scotland Yard's anti-corruption squad are said to have become concerned at the nature of some picture messages being exchanged.
Further investigation raised concerns that some of the messages were being sent while officers were on duty.
One line of inquiry is whether the exchanging of pornographic images took place during night shifts, with officers at different posts around Downing Street sending picture messages to one another.