Scotland Yard is investigating "whether or not criminal activity has taken place" following allegations of inappropriate behaviour towards women by Liberal Democrat peer Lord Rennard, it said tonight.

The news of police involvement came as pressure continued to mount on Nick Clegg, with party president Tim Farron admitting the party "screwed up" its response to allegations of improper behaviour by the party's former chief executive.

After initial denials that he was aware of complaints made by a number of women about Lord Rennard, Mr Clegg last night confirmed his office had heard "indirect and non-specific concerns" as far back as 2008, and had taken action at the time.

Tonight, a Scotland Yard spokesman said: "The Metropolitan Police Special Investigations Command has been approached by officials in the Liberal Democrat Party and is working with them to ascertain whether or not criminal activity has taken place."

The party announced tonight that the criminal lawyer Alistair Webster QC - a former chairman of the Liberal Democrat Lawyers Association - had been appointed to lead the formal internal investigation into allegations against Lord Rennard under the party's disciplinary rules.

The independent whistle-blowing authority Public Concern at Work will act as the main point of contact for anyone wishing to come forward with further allegations or information relating to the peer.

In a radio interview today, Mr Clegg said that "no very specific allegations" were put to him until a Channel 4 News investigation broadcast last week.

But the Daily Telegraph published a 2010 email exchange with Mr Clegg's chief of staff Jonny Oates, in which the paper gave details of the dates and locations of four alleged incidents between 2003 and 2007 involving the Lib Dem peer, and made clear it knew the identities of the women who had complained.

Lord Rennard has strenuously denied "any suggestion of improper touching" of women who he came into contact with in his role as chief executive.

Following the C4N broadcast, an investigation has now been launched under party disciplinary rules, while a separate independently-chaired review will look into how the Lib Dems dealt with the initial complaints.

Mr Clegg said that his former chief of staff Danny Alexander - now chief secretary to the Treasury - confronted Lord Rennard after concerns were raised anonymously in 2008 and warned him that any such behaviour was "wholly unacceptable". The peer firmly denied any wrong-doing.

Speaking to BBC Radio Solent days ahead of Thursday's crunch Eastleigh by-election, Mr Clegg said: "I totally understand people have got lots and lots of questions but I hope I have given a full, frank, honest account.

"I have got nothing to hide, the party has nothing to hide. We have now got to listen to the women who feel they weren't properly listened to and get to the truth and that is what we will do."

But the Telegraph published details on its website of an email sent to Mr Oates - then Lib Dem head of communications - in April 2010, spelling out the nature of the allegations and asking whether Mr Clegg was aware of them and whether it was true that Mr Alexander and Lib Dem MP Jo Swinson had looked into them.

Mr Oates responded at the time: "It is untrue to state that Mr Clegg was made aware of the incidents you allege. Given this fact, it is obviously untrue to state that Mr Clegg asked Jo Swinson or anyone else to carry out an investigation into the incidents that you allege."

Ms Swinson, now equalities minister, has now confirmed she did look into the women's claims, but was "careful to respect their wish for privacy and, for that matter, their right not to be harassed by the press".

Mr Farron acknowledged that the party had "screwed this up" and said a "completely full and open inquiry into how we got this wrong" was now under way.

"There are individuals out there who we had a duty of care towards and we did not fulfil that duty of care," the Lib Dem president told BBC Radio 4's Today programme. "That is something that we have to learn from, apologise for and make sure it never happens again."

Asked when he first heard of allegations against the peer, Mr Farron said: "A general rumour I heard a year or so ago but no specifics, not even who or what or when or anything."

Lib Dem deputy leader Simon Hughes, said that he "saw nothing and heard nothing that suggested there had been inappropriate behaviour" when he was party president from 2004-08. And the party's head of media from 2004-08, Mark Littlewood, told BBC2's Daily Politics that he heard "not a whisper or a sniff or a rumour" of the claims at the time.

Lord Rennard - a key adviser to a succession of Lib Dem leaders before standing down on health grounds in 2009 - has said he is "deeply shocked" by the allegations, which he "strongly disputes" and regards as a "total distortion" of his character.

In a statement on Friday, he said: "I absolutely deny any suggestion of improper touching, nor did I invite a woman to join me in my room.

"I am disappointed and angry that anonymous accusations from several years ago are once again being made public in this manner in a clear attempt to damage my reputation."