Hi Alex,
I found these examples on Amazon. Here's the link:
Binocular Digital Cameras
Looking more closely at the photos it seems the camera is in the centre and not integrated into the binocular optics.
I'm going to try to get a pair to try out for review purposes, as you can see there are a wide range of prices.
I can't imagine anything under £100 will be any good for recording birds. If you think about it, how much would it cost to get a half decent pair of binoculars and digital camera? Probably over £100!