It would appear that a wide range of tunes is used. It might be worth pointing out that old Grimes/Abram Brown etc is definitely a separate song to Josephus and Bohunkus allowing for a little bit of crossover. Both songs have been subject to the addition of commonplaces over time. Both are very widespread. In my native Yorkshire the 'Old Grimes' song has long been traditional in several quite different forms. 'Old Grimey/Old Johnny Walker' etc...