The survey shows that voters, including Labour supporters, rank Iraq last out of a list of 10 issues that they consider to be most important when deciding how they will cast their vote in the next general election. Only 12% say it is a crucial issue for them in deciding who to support.

Equally, the voters do not appear to share Westminster's preoccupation with the European Union and rank it only eighth out of 10.

Conservative voters do regard the future of the EU as a more important question to them than Labour voters, but it does not dominate their thinking about politics and they still rank it only sixth in their list of concerns.

The finding may give a jolt to those senior figures in the Tory party who regard a major crusade over changes to the EU constitution as the issue on which they can make the most progress at the next election.

Instead, the average voter overwhelmingly regards the state of the health service as the most influential factor in his or her decision, followed by education and law and order.

The polling evidence that Iraq fails to excite the voters may explain why Labour's poll position has remained buoyant over the past year despite the sharply divisive disputes within the cabinet and party over conduct of the war.

This month's figures on voting intentions continue that trend, with Labour - on 36% - recovering from the hammering it took in the June European elections, but its overall lead reduced from five points to three points as the Tories enjoy a slightly better month.

The August poll show the Conservatives up three points to 33%, mainly at the expense of the Liberal Democrats and the minor parties who have faded from public view after the European elections and subsequent byelections.

The share of the vote for the "other parties" has fallen from 13% in June to 9% this month, with Ukip the biggest casualties. Its share of the vote is down from 4% in the June Guardian/ICM poll to less than 1% this month.

When voters are asked what they consider to be the most important issues when deciding their party preference, their answers reveal an interesting profile of concerns. They were asked by ICM to name "two or three" that they considered the most important, so the percentages add up to far more than 100.

For all voters the health service - at 59% - dominates their concerns followed some way behind by education, on 42%, and then law and order on 35%.

The indication is that if the parties want to motivate people to vote in the next election they should concentrate on talking about public services and crime.

The traditional issues of the economy and government taxation and spending policies come next in their concerns, followed by the issue of asylum seekers, named by 20% of all voters.

Labour voters appear to be more interested in jobs than Tories or Liberal Democrats and they rank asylum, the EU and Iraq as the least important of their concerns.

Liberal Democrat voters rank the EU higher than other voters, but other polling data shows that this does not necessarily mean they share the party's pro-European outlook. They also rank Iraq higher than other voters in their concerns.