Nick Clegg has called for police to be allowed to "do their job" over allegations that senior Liberal Democrat peer Lord Rennard sexually harassed women in the party.

The Deputy Prime Minister hit out at "people who appear to want to act as self-appointed detectives", insisting the only way to get to the truth was to allow the two inquiries he set up to run their course and for Scotland Yard to carry out its investigations.

Speaking outside his home in south-west London, Mr Clegg told Sky News: "I understand there are many people who appear to want to act as self-appointed detectives trying to piece together events that happened many years ago, but the only way that we are going to get to the bottom of the truth ... is by allowing the two investigations that I established immediately after the Channel 4 broadcast to do their job and, indeed, to allow the police, whom we have now approached, to do their job as well.

"And in the meantime I cannot and my party cannot provide a running commentary on every shred of speculation about events which happened many years ago."

Police are investigating whether "criminal activity" took place following allegations of inappropriate behaviour towards women by the peer. "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," said a Scotland Yard spokesman.

Mr Clegg has come under sustained pressure to explain what exactly he had known about the claims and what he had done about them. He has insisted he has "got nothing to hide" but Lib Dem president Tim Farron, referring to the way the case had been handled, said the party had "screwed this up".

Lord Rennard, who was the Lib Dems' key election strategist and adviser to a succession of party leaders, has strongly denied the allegations made against him by a series of Lib Dem women.

A spokesman for Lord Rennard said: "Lord Rennard refutes these allegations. He will co-operate with any properly constituted inquiry. He has been notified of an internal investigatory panel within the Party. The matter must now be regarded as sub judice pending its proceedings and no further statement will be issued in the interim.

"He expects others to respect the sub judice principle, and he notes that under the party rules concerned it is for any case made against him to be proved by evidence to the requisite standard. He denies impropriety.

"He would reiterate that in 27 years of working for the Liberal Democrats he received no complaint or allegation about his behaviour. Nor is he aware of any personal complaints being made in the three and a half years since he stood down as chief executive until last week."