Scandal-hit peer Lord Sewel has resigned from the House of Lords after coming under intense pressure over footage of him allegedly taking cocaine with two prostitutes.

The former Labour minister - who is the first peer to stand down in disgrace following new rules introduced last year allowing resignations from the Upper House - apologised for the "pain and embarrassment" caused by the drugs and sex scandal, exposed in the Sun on Sunday.

The married 69-year-old had earlier quit his £84,500-a-year role as deputy speaker of the Lords and chairman of the Lords Privileges and Conduct Committee, but until this morning was resisting calls for him to leave Parliament altogether.

Last night the Metropolitan Police raided Lord Sewel's home with a sniffer dog and battering ram.

A group of officers searched the flat for three hours and left carrying several bags of evidence as part of their investigation into "allegations of drug-related offences involving a member of the House of Lords".

In a statement to parliamentary officials announcing his resignation, Lord Sewel said: "I hope my decision will limit and help repair the damage I have done to an institution I hold dear ... I want to apologise for the pain and embarrassment I have caused."

Prime Minister David Cameron welcomed his decision to "absent himself" but played down the prospect of further reform of the Second Chamber, saying there was "no point in trying that route again" after the failure of proposals under the coalition.

Conservative Leader in the House of Lords Baroness Stowell said: "I welcome Lord Sewel's decision to resign permanently.

"For the House of Lords to earn the confidence of the public, all of us must respect the privileges that come with a peerage and recognise that - because we are unelected - it is especially important to meet the standards the public have a right to expect, and to act swiftly when we fail."

The Sun newspaper has now alleged that Lord Sewel boasted to prostitutes about sleeping with a BBC presenter - something the woman involved has emphatically denied.

Sewel is said to have admitted that he committed adultery with 13 women over 17 years.

The scandal had fuelled criticisms the unelected House of Lords is out of touch and should be scrapped.

The chamber has swollen in size in recent years, and there are currently 783 members, making it the largest legislative assembly outside China.

Speaking in Singapore, Mr Cameron appeared to confirm that he plans to use the upcoming dissolution honours to add further Conservative Lords in order to redress the current imbalance which leaves the 226 Tories in a minority despite their victory in the general election.

"It is important the House of Lords in some way reflects the situation in the House of Commons," said the Prime Minister. "At the moment it is well away from that. I'm not proposing to get there in one go but it is important to make sure the House of Lords more accurately reflects the situation in the House of Commons."

Lord Hill of Oareford, Tory former leader of the Lords, said Lord Sewel's decision to step down was "better late than never".

He told the BBC Radio 4 Today programme: "His position wasn't tenable. I am glad he's had a change of heart. I think if you are responsible for the setting of standards you yourself have to make sure you deliver on that."

Liberal Democrat president Baroness Brinton told BBC2's Victoria Derbyshire programme: "There's a feeling of relief that he's finally understood the damage that he's done.

"It's not just about the police investigation on the drugs and prostitutes, it's also about the very sexist and racist comments he made about Asian women.

"That, with his leadership role in holding every peer to account for his conduct, meant his resignation was inevitable."