There are some scattered references to a "Burgundy Cocktail" on Google, but
they all seem to follow the general formula of 3 parts burgundy, 1 part
cognac, and 1 part of some sort of cherry brandy -- no gin in sight. The use
of cherry brandies suggests that that drink probably dates to the early 20th
century, but I didn't see any references in my cursory search of the old books
I can find on the internet.
If the original order was indeed for a Beefeater Burgundy, my best guess would
be to try something along the lines of a sweet or perfect martini. I'd
suspect, though, as you did that the order got garbled somewhere.