I might be wrong, but I think the meaning of "fireman" are crucial to unravel this joke - please see the second explanation of the word here: http://www.urbandictionary.com/define.php?term=fireman; as for the rest, I'd better leave it to your own imagination...
first we need to talk about 'soldier's finger', this is a kind of british breakfast, short bread dip in the half boiled egg.
now if you look at the joke then you should understand.