Ah, now. I have always taken it that The Barley Mow was the name of the pub where the song was being sung & all those drinking vessels were in use and all these people were to be found; and the 'company' were the drinkers present. It is, still, a common pub name ~~ google "Barley Mow pub" and see how many come up.

barley mow public house -- About 29,100 results (0.19 seconds)

Hic*

~M~

*except that I don't actually drink' but you know...