The Lord Speaker issued a strongly-worded statement in which she said Scotland Yard would be asked to investigate.
Baroness D’Souza said: "Today’s revelations about the behaviour of Lord Sewel are both shocking and unacceptable.
"Lord Sewel has this morning resigned as Chairman of Committees.
"The House of Lords will continue to uphold standards in public life and will not tolerate departure from these standards.
“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."
In footage published by The Sun on Sunday, the 69-year-old peer is said to have stripped naked in front of the pair in his flat near Westminster last week.
Hunched over a table, the former Labour minister for agriculture, environment and fisheries is pictured with a rolled-up bank note in his hand as he appears to snort white powder.
The peer's third marriage, to Lady Jennifer, 54, took place in 2005.
He is seen in the video footage with his wedding ring on show.
One of the escorts is said to have told Lord Sewel: "You're such a party animal!", before he allegedly replied: "I know. Disgusting, isn't it?"
He is alleged to have snorted three lines of cocaine during the 45-minute session.
Lord Sewel speaking in the House of Lords
Lord Sewel, a former senior vice principal of Aberdeen University, received £84,525 as chairman of the Lords' Privileges and Conduct Committee - the body that upholds standards of behaviour among peers.
A Scotland Yard spokesman said: "We are aware of allegations in the Sun and any allegations that are made will be investigated.
"We are aware that Baroness D'Souza has indicated she will be making an approach to the Metropolitan Police and we will get on the case in due course."
A House of Lords spokesman said: "Lord Sewel has this morning resigned as chairman of committee, a salaried role.
"This means he is no longer in an official role.
"I do not yet know whether he intends to retire from the House, which is now possible under the rules."
Earlier this month, he wrote a blog for the Huffington Post website in which he spoke about the House of Lords' new powers to banish peers who breach the code of conduct.
"The actions of a few damage our reputation," wrote Lord Sewel.
"Scandals make good headlines.
"All members now sign a declaration to obey the code and the seven principles of public life.
"The requirement that members must always act on their personal honour has been reinforced.
"No system of regulation can be perfect, but the House of Lords has come a long way since 2010 in improving its regulation of its members and punishing the small number who misbehave.
"Today's new sanctions strengthen the regime further."
Lord Sewel declined to comment to The Sun on Sunday about the footage said to have been filmed at his flat in Dolphin Square.
He was a Labour peer until resigning his party membership to take up the House of Lords role, and is formally known as a "non-affiliated member".
A Labour spokeswoman said: "He is not a Labour peer so we are not commenting."
As a junior lecturer at Aberdeen University in 1975 Lord Sewel published the book Colliery Closure and Social Change and lists his recreations in Who's Who as hill-walking, skiing and watching cricket.
His first marriage to Rosemary Langeland took place in Malvern, Worcs, in 1968 and they had a son, now 38, and a daughter, now 36, who were both born in Aberdeen.
Lord Sewel's second marriage was in 1988 to Leonora Harding, in Aberdeen, with the third to Lady Jennifer 10 years ago also taking place in the city.