Once pre 9/11 I managed to get a 15 second check in....I walked up to what I thought was empty desk and the girl said without looking up, okay here's your boarding pass, you're all set.

She then looked up and apologised, she had thought I was someone else, who had been checking in but had dashed off to the restroom.

Managed 5 mins from the approaching the BA check in queue at Paddington to boarding the HEX once. Details here.