The Conservatives should no longer count on winning the election outright, according to a Guardian/ICM poll published today.

The new survey suggests Britain is on course for a hung parliament amid faltering public support for David Cameron's party.

The opposition have also lost ground on key policy issues, including the economy, and in particular may be losing their campaign against Labour's so-called "death tax". Labour leads the Tories by eight points as the party with the best policy on care for the elderly.

The two parties are neck and neck on their ability to sort out the economic crisis, against a nine-point Tory lead when the question was last asked in August 2009.

With no more than three months to go until polling day, the Conservatives have fallen to 37%, down three on last month's Guardian/ICM poll and down two on another ICM poll earlier this month.

The party has not fallen so low in an ICM poll since the tail end of the banking crisis, last falling to 37% in February 2008.

As recently as last October the Tories hit 45% in an ICM poll and the party will be alarmed by this latest evidence that the race is tightening, which confirms the findings of some other recent polls.

Meanwhile Labour's support, at 30%, is eight points up on its absolute ICM bottom last May, and slightly above its average for the second part of last year. However, there is no sign of either a boost for the party following Gordon Brown's Piers Morgan interview or a fall after this weekend's reports about Brown bullying his staff.

Labour's support is up one point on the last Guardian/ICM poll and unchanged from the most recent ICM poll. Research began last Friday and most was carried out before the serialisation of Andrew Rawnsley's book in yesterday's Observer, which may have affected Labour support. Around a fifth of responses were collected on Sunday.

Nick Clegg's hopes of a powerful place in a hung parliament are also boosted by today's poll, which puts the Liberal Democrats on 20%, unchanged from the most recent ICM and down one on last month's Guardian poll.

All this suggests that Labour and the Lib Dems are holding steady while the Conservatives lose some ground to smaller parties, which are on a total of 13%. Nationalists are on 5%, Ukip and the Greens on 3% each and the BNP on 2%.

Estimates of what these shares would mean for the parties on polling day vary, but a 7% lead is at the margins of what the Tories think they need to win a majority. One academic calculation suggests the result would leave Labour only 25 seats behind the Tories in a hung parliament, although any improved Tory performance in marginal seats would offset that.

• ICM Research interviewed a random sample of 1,004 adults by telephone on 19-21 February 2010. ­Interviews were conducted across the country and the results have been weighted to the profile of all adults. ICM is a member of the British Polling Council and abides by its rules