Sewel, whose responsibilities included upholding standards in Westminster, also appears set to face a police investigation over the scandal.
"Today's revelations about the behavior of Lord Sewel are both shocking and unacceptable," Baroness D'Souza, the speaker of the House of Lords, said in a statement Sunday. "Lord Sewel has this morning resigned as chairman of committees."
In one scene, the edited video that was published by The Sun on Sunday
, a British tabloid newspaper, appears to show Sewel inhaling a line of white powder with a rolled up 5 pound note.
The video also includes snippets of conversations allegedly between Sewel, who is married, and the female sex workers. In the dialogue, he seems to make a thinly veiled reference to cocaine, as well as a derogatory remark about women.
The Sun reported that the events depicted in the video, as well as other compromising acts, took place in Sewel's London apartment near the UK Parliament in recent weeks.
"These serious allegations will be referred to the House of Lords Commissioner for Standards and the Metropolitan Police for investigation as a matter of urgency," D'Souza said.
Attempts by CNN to reach Sewel for comment Sunday and Monday were unsuccessful.
The House of Lords Press Office said Monday that Sewell had sent a written request for a leave of absence from his seat in the chamber, of which he has been member since 1996.
"I also wish to make clear that in doing so I have no intention of returning to the House in any way until the current investigations have been completed, when in the light of their outcome I will review my long term position," Sewel said in the request.
London's Metropolitan Police Service said Monday that it had taken charge of an investigation into the matter.
"I think it's right he's stood down from his committee posts, and I'm sure further questions will be asked about whether it is appropriate to have someone legislating and acting in the House of Lords if they have genuinely behaved in this way," Prime Minister David Cameron said.
Sewel had choice words for Cameron on the undercover video, calling him the "the most facile, superficial Prime Minister there has even been."
As chairman of committees of the House of Lords, Sewel was responsible for supervising the activities of the chamber's assorted committees, including the one for privileges and conduct.
A new parliamentary code that he championed just this year requires members to act in the public interest and with integrity. Lord Sewel could be the first peer to be formally tested on those guidelines.
The chairman of committees is first among a panel of 20 to 25 deputy speakers
in the House of Lords. Sewel, whose full name is John Buttifant Sewel, had held the politically independent position since 2012.
Before that, he was on the side of the Labour Party, serving as a government minister between 1997 and 1999. During that time, he worked on efforts to set up the new Scottish Parliament.
The Labour Party, now in opposition, said it had suspended Sewel following the allegations in The Sun.