John Buttifant Sewel quit as deputy speaker of the House of Lords two days after The Sun on Sunday released footage showing him semi-naked and snorting powder through a banknote while partying with two women.
In a statement, Sewel said his behaviour might not have breached the Lord's code of conduct.
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"The bigger questions are whether my behaviour is compatible with membership of the House of Lords and whether my continued membership would damage and undermine public confidence in the House of Lords," he said.
"I believe the answer to both these questions means that I can best serve the House by leaving it."
Sewel, 69, who is married, was in charge of standards and discipline in the upper chamber.
Commentators said his case would spur calls to overhaul the House of Lords, a chamber which with over 800 members critics say is becoming too big because of the sitting prime minister's right to regularly swell its ranks with political appointees.
"Now Get Rid Of The Lot Of Them", the left-leaning Mirror newspaper said on its front page on Tuesday.
"The discredited House of Lords should be consigned to history where it belongs," the paper said in its editorial.
Less than two weeks previously, Sewel had written an article boasting how the House of Lords had taken steps to protect its image. He had said only a small number of lords broke the rules and that most understood that personal honour came first.
In his statement on Tuesday, he said: "I hope my decision will limit and help repair the damage I have done to an institution I hold dear. ... Finally, I want to apologise for the pain and embarrassment I have caused."
Editing by Louise Ireland.
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