Ed Miliband ends his first week as Labour leader with his party ahead of the Tories in a Guardian/ICM poll for the first time since Gordon Brown ducked the chance of holding an election in 2007.

But the two-point lead is the result of a slump in Conservative support rather than any surge in Labour backing and the poll suggests voters are giving Miliband a wary rather than an enthusiastic welcome.

The results will offer him a morale boost at the end of a tumultuous week but they also suggest that many Labour supporters are yet to see their new leader as a potential prime minister, and that his brother David might have attracted more support in the short term.

The poll also shows that the public mood is swinging against the scale and speed of spending cuts, with 43% now saying the cuts have gone too far compared with the 37% who think the balance is right. By contrast, in July 39% thought the balance right, and 38% said too far.

Carried out after Miliband's conference speech, but largely before his brother announced he was pulling out of the shadow cabinet, today's poll puts Labour on 37%, unchanged on last month. The Conservatives have dropped two points to 35% – down from a post-election high of 41% in June – and the Liberal Democrats are unchanged on 18%.

All three parties can draw comfort from these figures, although the Tories may be dismayed to see their poll rating drop further even before next month's announcement of deep spending cuts.

There has been a shift of opinion in Labour's favour since May, with support up almost eight points at the expense of the Lib Dems. Almost one in four people who voted Lib Dem are now thinking of voting Labour instead.

Nick Clegg will be relieved, however, that today's ICM poll does not find the collapse in third party support shown in online polls. Lib Dem support is unchanged on the level in September 2009.

Labour's new leader has so far had little chance to make an impression. Among definite Labour voters only 52% say Ed Miliband would make the best prime minister of the three party leaders while 24% name David Cameron. By contrast, 89% of Conservatives pick Cameron. More Lib Dem voters also back Cameron as a competent prime minister than back Clegg. Among all voters, 20% think Ed Miliband would make the most competent prime minister, compared with 47% who say Cameron and 10% Clegg.

Today's poll finds a marginal preference among voters for David Miliband over his brother. Most voters say that the arrival of either of the brothers would have made no difference to their attitude. But among those who say the choice does make a difference, positive support for Ed outweighs negative by one point. For David, the positive lead would have been nine points – with people who voted Conservative in the general election among those more attracted to the defeated candidate.

There is evidence that voters see the man denounced by his press enemies as "Red Ed" as more leftwing than Tony Blair or Gordon Brown. Asked whether they think Ed Miliband will take the party to the left, the right or make no difference, 28% say to the left against 41% who think he will keep it in the centre and only 8% to the right. Labour supporters who think the party will move to the left overwhelmingly welcome the possibility. So do many Lib Dems: 61% of those who believe Labour will shift to the left support the move.

Despite anxiety about cuts, the coalition remains trusted overall on the economy. Asked, regardless of their own loyalties, whether they think the government or Labour is best placed to ensure a prosperous future, 50% pick the coalition and 31% Labour. But some former Lib Dem voters are having second thoughts about their party's policies now it is in power: 24% of the people who voted for the party in May now back Labour's economic plans.

The idea of coalition government appeals to many but most would still like to see their own party in power. Of the likely outcomes at the next election, 26% think Labour on its own would be best for Britain, 19% the Conservatives on their own, 21% a continued Con-Lib coalition and 13% a Labour-Lib Dem deal.

Only 50% of Tory supporters want their party to rule alone, while 41% want coalition with the Lib Dems, which suggests Cameron will face little dissent from the grassroots at conference next week.

• ICM Research interviewed a random sample of 1,005 adults aged 18+ by telephone on 28-29 September 2010. ICM is a member of the British Polling Council and abides by its rules.