And he denied that the incident was in any way linked to sex or drugs.
Mr Davies told police he was robbed at knifepoint after meeting a stranger as he strolled on Clapham Common and accepting a dinner invitation on Monday night.
He then collected another man and a woman before driving to Brixton, where the three passengers turned on him, taking his car, wallet and phone.
Four people arrested in connection with the inquiry remain on police bail but inquiries are continuing, police said.
A man is due to appear in court on Saturday morning charged with robbing Mr Davies of his car and its contents.
Speculation about the reasons behind his resignation have sparked a series of stories in the press.
In a television interview on Friday, Mr Davies said the circumstances leading up to his robbery at knifepoint were "bizarre", and a "gross error of judgement".
But he did not go into any more detail about the circumstances behind the incident.
He said: "It was a moment of madness for which I have subsequently paid a very, very heavy price and I am deeply sorry. I bitterly regret it."
In his first full media interviews since his resignation, Mr Davies refused to discuss questions about his private life. But he said: "I have a very long-term, loving, stable relationship with my wife, who has been marvellously supportive of me this week."
Shock and trauma
Speaking in South Wales, Mr Davies also denied the prime minister and other party leaders had pressurised him into resigning from the Cabinet and standing down as Labour's prospective leader of the Welsh Assembly.
"Tony Blair was very, very supportive and understanding, and I am deeply grateful for the way he has handled this matter as far as I am concerned."
Mr Davies, looking tired and red-eyed, said he was still suffering the effects of shock and trauma "after a pretty horrific experience" during the robbery.
Handy reminder?
Mr Davies went into his television interviews with the word "sorry" written in block capitals and black ink on the back of his left hand.
The MP's reminder note to himself was being widely interpreted as a sign of what he had intended to tell viewers as he once more denied gay sex or drugs were behind his resignation.
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