As far as I understand it its not an opinion poll, its simply a poll of viewers. Its like asking the crowd at Old Trafford who the greatest team in the world is.
Not sure why you think that,
YouGov &
ORB polls both show 2/3 of people support additional air strikes in Syria.
Its important to remember that its mainly social liberal Labour supporters that were traumatised by the Iraq war. Lots of other people opposed the war, but really don't see it as the grave lesson that Labour's left think it is. I'm sure Osborne and Cameron are aware of the political lessons from Iraq, hence their decision not to take a unilateral decision on air strikes. On the other hand, they'll look at Blair's intervention in Kosovo (which Corbyn opposed btw) and see how that led him to international acclaim.
I'd also disagree with your opinion on the military in working class communities. No parent wants a child off in some war of course, and no-one wants british soliders dying needlessly. But to believe that the military, and military action, are unpopular is to misunderstand the outlook of social (small c) conservatives, which most working class communities tend to be. Far from being some neccesary evil, the millitary is intimately tied in to the social conservative mindset.
Its a measure of Britain's importance in the world, its strength, its ability to stand up for itself. Rather than being unpopular among the working classes, its a source of nationalistic pride to have a military that has a place on the international stage.