I'm not totally familiar with the British so there may be parts that aren't quite like the Presidential veto. But, what about a Declaration of War?
Let's say that Parliament has a bunch of members calling for war. The declaration passes, but then the Queen, who is acting as a mediator, suspects that the sides are really close and so she veotes this before the military can be mobilized.
The only problem is, who else is negotiating for the British and why aren't they back in Parliament debating the declaration. I'm thinking it could be along the lines of a book i read where the U.S. Cabinet was debating a declaration of war against the Soviets at the very end and some were insisting the president was dead, and he comes in at the end and says "no he isn't," and goes on to explain why the supposed disappearance was planned. ("The President's Plane Is Missing" perhaps?) But, I don't know if that would necessarily be similar in the British system.
But, I *think* it could happen. Although you could argue that this goes back to the "government passes a bill then asks the Queen to" thing.