LONDON (REUTERS) - British Deputy Prime Minister Nick Clegg on Sunday denied covering up allegations of sexual misconduct by a former senior member of his Liberal Democrat party, already floundering in opinion polls.

Allegations of sexual impropriety by former party chief executive Chris Rennard threaten to engulf Mr Clegg and further undermine the Liberal Democrats, the junior member of Britain's coalition government.

The latest furore comes at a bad time for the party, after the resignation of cabinet minister Chris Huhne this month who admitted he had asked his then wife to accept a penalty for a 2003 speeding offence he had committed.

A local election to replace Huhne is to be held on Feb 28.

Mr Rennard, the mastermind behind the party's election strategy before quitting in 2009, was accused in a report by Britain's Channel 4 television channel on Thursday of inappropriately touching female party members and activists several years ago.

The report has since triggered a flurry of similar allegations in the British media.

Lawyers for Mr Rennard, a member of parliament's upper house, said after the Channel 4 report that he was "deeply shocked by and strongly disputes" the allegations made against him.

Media reports have since then accused Clegg of knowing of the allegations long ago but not investigating them.

"I am angry and outraged at the suggestion that I would not have acted if these allegations had been put to me," Mr Clegg said late on Sunday, rejecting suggestions of a "cover up".

He said was made aware of "indirect and non-specific concerns" about Mr Rennard in 2008, and had acted on them, but there was a limit to how far the party could take the matter given sources of the concerns were indirect and anonymous.

The Liberal Democrats have announced two internal inquiries since more detail has come to light, one into how the party handled the allegations, and another into the allegations themselves.

Mr Clegg said they would reveal the truth of what happened.

"But in the meantime, I will not stand by and allow my party to be subject to a show trial of innuendo, half-truths and slurs," Mr Clegg said.

Britain's opposition Labour party demanded an independent investigation.

"This series of allegations are too serious to allow the Liberal Democrats to investigate themselves," said Labour lawmaker Bridget Phillipson.

"Nick Clegg and other senior Liberal Democrat lawmakers and officials must come clean about what they knew and what action was taken about these serious allegations," she added.