Well, we don't know, but they could have received x piece of intelligence, then acted on that immediately.
It's not as though Dave has a mobile with which to directly call each country's head of government - if an immediate decision had to be made, there wouldn't have been time to get through to the Italian ambassador, then to the decision makers re: this kind of issue, then get the message back again. Even if that conversation did happen - if the Italians said no, why would it stop us? Two hostages, one Brit, one Italian. One side wants to go in, the other doesn't. We're not going to abort because the other party says no, when we believe they're in immediate danger of death.
I didn't mean to imply that we should wait for Italian consent, but it would be somewhat... err... polite to inform them to the best of our ability. You're right in that there might not have been any time and if so I'd expect us to say 'sorry, there was no time'.
I heard an ex-CIA guy on BBC news slamming the British on this... but I was thinking, ex-CIA, what does he know?

