He literally swallowed it down whole
he must have opened his throat like a snake does 
We know this because I heard him vomiting, very loudly. I sent DH to check (as you do) and he found cat sick with an entire intact bird in it. DH admits he is no Chris Packham so couldn't identify the bird but it was bigger than a Robin but smaller than a blackbird. He thought about 5 inches long
which is bloody big to swallow whole.
I have always had cats and have never ever heard of a cat doing this. Apart from being seriously grossed out by it I'm worried that he might choke if he does this again. Or damage himself internally? And I thought he didn't catch birds! Has anyone else come across this?