Did the Iraq War play a significant role in the defeat of Labour? Blair, one of the main architects of that war, managed to win re-election in 2005. IIRC, that was after the war had begun to go snafu, and it had become apparent that the original rationale for the invasion didn't hold water.
The Iraq War played a big part in the unpopularity of Labour towards the end. Whilst in 2005 it might have begun to seem a mess, it wasn't actually that clear at the time. Also, 2005 represented a major failing by the Conservatives to put across a clear and compelling message to the electorate.
By 2010 Labour had had Iraq hang around its neck for five years.
But it also had the financial crisis to contend with, as well as voter apathy and desire for change.
I don't think its too hard for Labour to get a plurality in a hung parliament in 2010 and many Lib Dem party members would have preferred to prop up a Labour Government than a Tory one.
A few down-the-road changes to consider:
*The legacy of Tony Blair (and to a lesser extent Brown) are going to be very different. Whilst the party might feel the need to tweak New Labour formulas, the Blair era will be considered THE model for progressive government in decades to come for the party. You wouldn't see anything like the Corbyn-surge IOTL. Blair would be a respected party elder ITTL - same for other Blair-era figures such as Mandelson.
*You could well see the Conservatives splinter if Cameron fails - Tory leadership battles are bloody historically and in this scenario nothing has butterflied the appeal of Farage and UKIP.
*The Lib Dems probably get their boundary changes and AV ITTL. Labour was much more undecided on the issue than Cameron - probably Clegg is more of a power-player in years to come.
*The SNP is still lurking in the wings, however, as again this scenario does little to limit their appeal in Scotland. They are, even more than in our timeline, a timebomb waiting to explode any fragile Labour coalition come election time in 2015.
*Without the legacy of Iraqi intervention hanging over them, Labour is probably less gun-shy about intervention in Syria. It becomes a more black and white issue especially as France (presumably in this timeline much closer to the UK as they both protest the Iraq War) is going to bomb.
*Just my opinion, but I feel that Blair/Brown/whoever by 2015 would have handled the Syrian refugee crisis better. Even the most charitable of assessments must see Cameron as having dropped the ball on this, and whilst people will probably flame me for this in the thread Iraq aside Blair actually had (and arguably has) impressive humanitarian credentials.