Sewel had already quit a senior post in the House of Lords
, the second chamber of the UK Parliament, and is facing a criminal investigation after video emerged over the weekend that allegedly showed him taking drugs with prostitutes.
In the statement released by the House of Lords on Tuesday, he said he had terminated his membership of the chamber.
"The question of whether my behavior breached the Code of Conduct is important, but essentially technical," Sewel said. "The bigger questions are whether my behavior 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.
"I believe the answer to both these questions means that I can best serve the House by leaving it," he said.
The photos and edited video published by The Sun on Sunday
, a British tabloid newspaper, appeared to show Sewel in a series of compromising acts that included inhaling a line of white powder with a rolled up 5 pound note.
The video footage also contained snippets of conversations allegedly between Sewel, who is married with children, and the female sex workers.
In the dialogue, he seemed to make a thinly veiled reference to cocaine, a derogatory remark about women and disparaging comments about past and present world leaders. Pictures showed him apparently taking drugs off a woman's chest and wearing an orange bra.
"I want to apologize for the pain and embarrassment I have caused," Sewel said in his statement Tuesday.
CNN has not been able to reach Sewel directly for comment.
The speaker of the House of Lords, Baroness D'Souza, said in a statement Sunday that Sewel's reported behaviour was "shocking and unacceptable."
She said at that point that Sewel had resigned from the position of chairman of committees, a key oversight role in the chamber, and that the allegations against him would be referred to police.
London's Metropolitan Police Service said Monday that it had launched an investigation.
A new parliamentary code that Sewel championed just this year requires members to act in the public interest and with integrity.
"As a subordinate, second chamber, the House of Lords is an effective, vital but undervalued part of our political system," his statement said. "I hope my decision will limit and help repair the damage I have done to an institution I hold dear."
He had been a member of the chamber since 1996 and held the position of chairman of committees since 2012.
Between 1997 and 1999, Sewel served as a minister for the Labour government of Tony Blair, who was Prime Minister at the time. In that role, Sewel worked on efforts to set up the new Scottish Parliament.