LONDON (AFP) - British police on Monday said they would probe claims of sexual impropriety by a former CEO of Britain's Liberal Democrats that threaten to engulf party leader and deputy prime minister Nick Clegg.

Metropolitan Police announced in a statement on their website that they were investigating claims made by four women against Mr Chris Rennard to see "whether or not criminal activity has taken place".

The message revealed that the force had been "approached by officials in the Liberal Democrat Party following recent media reporting".

The Liberal Democrats' popularity has plunged since Mr Clegg signed an agreement with the Conservatives, making them the coalition government's junior partners following the 2010 election.

Mr Clegg admitted he was aware in 2008 of "indirect and non-specific concerns" about Mr Rennard, but denied newspaper reports that he ignored multiple claims of sexually inappropriate behaviour against the peer.

Mr Rennard, who now sits in parliament's upper House of Lords, "categorically denied that he had behaved inappropriately and he continues to do so", Mr Clegg said on Sunday.

Channel 4 News last week aired claims against Mr Rennard made by four women going back 10 years.

Two of the women accused the peer of inappropriately touching and propositioning them.

The revelations come at a bad time for the ailing party as it fights to hold onto a crucial parliamentary seat in a by-election due to be held later this week.

The vote in Eastleigh, south England, pits them against their senior coalition partners.