Story highlights "I want to apologize for the pain and embarrassment I have caused," Lord Sewel says in statement

He announces he has terminated his membership of the UK's House of Lords

A video released over the weekend allegedly showed him taking drugs with prostitutes

(CNN) Scandal-hit British lawmaker Lord Sewel has stepped down from parliament and apologized for "the pain and embarrassment" he has caused, according to a statement Tuesday.

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.

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