Here the word "drudge" means "toil", or "do hard work": http://www.merriam-webster.com/dictionary/drudge. It's not so commonly used these days (so I'd imagine that this is a relatively old quote) but still makes sense ('drudgery' is still in relatively common usage, at least in the UK).
From the context of "behind a gun", I'd assume that the author is speaking about the Battle of Trafalgar, rather than about Trafalgar Square. Since that was a naval battle, "gun" would be referring to a ship's cannon rather than some kind of handheld weapon. So another way of putting the last part of the example would be to change
drudge behind a gun at Trafalgar
work behind a cannon during the Battle of Trafalgar.