But you said yourself
"albeit after being fed a pack of lies", so the votes are not a reliable indicator of what would've happened in a Conservative alternative reality, and we really have no way of knowing what would've happened in that circumstance.
Here's why I think it's unlikely we would've gone to war if the Conservatives would've been in charge.
Firstly, the cabinet would've contained a number of people, particularly the most senior, who were in government for the 1991 war, so they would've known exactly why we didn't go further back then, thus there would've been an inbuilt bias against the war that was not present in Blair's cabinet.
Secondly, to go to war in the circumstances required two things:
- a Prime Minister deranged enough to believe he could rebuild the Middle East into some kind of happy-clappy Western democracy through the force of his own personality, and who was happy to lie through his teeth to both parliament and the country to achieve this;
- a communications director who was happy to do the same and willing to manipulate intelligence material in a way that essentially turned it into an outright lie;
neither of which I believe would've been present in a Conservative administration at the time.
Thirdly, I suspect the Conservative backbenchers would've presented a much formidable opposition than they were in opposition, Labour would perhaps have opposed the war, the BBC and others would've been much more critical, so any justifications for the war would've been subject to much more scrutiny, and would likely fall apart as a result.
Finally, I can't see a Conservative AG being willing to be "persuaded" to offer a legal opinion suggesting that the war was perhaps legal, and I can't see the cabinet being fobbed off with that either.
So if a Conservative PM had tried to push ahead with the war, he would likely have lost any vote in the house, been faced with mass resignations from his cabinet, and would've been removed from office within days.