A low-tech solution might be to turn on a radio, softly enough so that it doesn't cover over the barking, but loud enough so that when the station identifies itself, or an announcer declares the time, that audio will be recorded on the same track as the barking.
The problem with internal timestamps is that they can be edited in or otherwise spoofed. The dog's owner might be able to claim that you didn't make the recording when you say you did.
A radio time signal is completely external and therefore probably pretty good evidence. If you have a shortwave radio you could tune in one of the world time-broadcasting stations, such as the US WWV or Canadian CHU -- there must be one in the British Isles. Greenwich? Anyway, that audio would give you 1 minute time signals.
A person arguing against you would have to be able to show that you had somehow added a track or laid the time signal over the barking. An audio engineer would be able to show that you didn't, if it ever came to that.
