I have experienced pretty much this exact scenario! William Morris Club in Wimbledon 1988, and it was 7" single. The dog was well behaved at least.
Another time, about ten years later, with a different band, after a couple of pretty successful dates in the autumn, we were booked to play the small room at the Mean Fiddler on 2nd or 3rd January, so everyone was still recovering from New Year.
What's more it was a Tuesday night, freakishly cold (something like -7C IIRC) and quite windy to boot.
Unsurprisingly, I think we had about three people in the audience. I took a peep into the main room and even the headline act had pulled about ten people in.
We were told shortly after that The Fiddler wouldn't be booking us any more because we were not able to get enough people along.