Downing Street said in a statement: "Peter Hain has made his statement. The Prime Minister has accepted Peter Hain's resignation. There will be an exchange of letters in due course."
It is understood that Mr Hain phoned the Prime Minister at around 11.30am and informed him he had been told by the Electoral Commisssion of the police investigation.
Mr Hain is understood to have offered his resignation at that point without hesitation.
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