The Liberal Democrats have slumped to their lowest-ever poll rating in the wake of allegations that their former chief executive Lord Rennard sexually harassed female party activists.

For the first time in its monthly polls for The Independent, ComRes puts Nick Clegg's party in fourth place behind the UK Independence Party. The Liberal Democrats are on just eight per cent, down two points on last month, while Ukip is on nine per cent (down one point).

The survey, taken between Friday and Sunday when the Rennard controversy dominated the headlines, suggests it has damaged the Liberal Democrats. It is a setback for Mr Clegg in the run-up to Thursday's Eastleigh by-election caused by the resignation of Chris Huhne, the former minister who has admitted perverting the course of justice and awaits sentencing.

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Scotland Yard tonight said it had launched an inquiry into allegations made against Lord Rennard. In a statement, the Metropolitan Police said it had been approached by party officials to investigate the claims that have surfaced about the peer in recent days. It added: "We are working with them to ascertain whether or not any criminal activity has taken place."

Senior Liberal Democrats had been confident of victory over their Conservative coalition partners but now admit privately that their prospects could be harmed by the party's handling of the allegations against Lord Rennard, which he denies.

According to ComRes, Labour has extended its seven-point lead last month to 12 points, its biggest since 2005 in a ComRes poll for this paper. Labour is now on 43 per cent and the Conservatives on 31 per cent (down one point). Other parties are on nine per cent (no change). The Tories' standing may have been damaged by the news on Friday evening that the ratings agency Moody's had downgraded the UK's triple-A credit rating.

If repeated on a uniform swing at a general election, these figures would give Labour an overall majority of 122. The Liberal Democrats would lose 39 seats, leaving them with just 18 MPs.

Only one in three people (33 per cent) who voted Liberal Democrat in 2010 say they would do so now; 40 per cent of them would support Labour. Some 82 per cent of those who voted Tory at the last general election would back the party now, although eight per cent say they would switch to Ukip now. Labour has retained the support of 92 per cent of its 2010 voters.

A survey of 1,000 people in Eastleigh by the Daily Echo newspaper showed the Liberal Democrats and Tories neck-and-neck on 22 per cent, with Ukip in third place on 18 per cent and Labour trailing in fourth spot on 12 per cent. A further 22 per cent said they would not vote.

A poll published today by Lord Ashcroft, the former Tory deputy chairman, gives Mr Clegg's party a five-point lead in Eastleigh. The survey of 1,000 people puts the Liberal Democrats on 33 per cent, the Tories on 28 per cent, Ukip on 21 per cent and Labour on 12 per cent.

ComRes interviewed 1,005 GB adults by telephone between February 22-24. Data were weighted to be demographically representative of all GB adults. Data were also weighted by past vote recall. ComRes is a member of the British Polling Council and abides by its rules.

If repeated at a general election the figures would give Labour a majority of 122 seats