Defence Secretary Liam Fox resigned yesterday after a week of allegations over his working relationship with friend and self-styled adviser Adam Werritty.
Fox was being investigated amid claims he broke the ministerial code.
In a letter to David Cameron, Fox said he had "mistakenly allowed" personal and professional responsibilities to be "blurred".
In response, the prime minister said he was very sorry for Fox's departure but "understood his reasons".
Fox has been under pressure since it emerged that Werritty, a lobbyist, had met the defence secretary on 18 foreign trips despite having no official role, and had been handing out business cards suggesting he was an adviser to Fox.