He first appeared in the British comic 'Super Spider-man and Captain Britain #243' looking like this...
He next appeared in Captain Britain's solo comic in the 80's with a different costume, and obsessed with Captain Britain, and his defeat, a typical arch-enemy thing to do. All of this written by Alan Moore, and Drawn by Alan Davis.
Alas the whole Slaymaster hates Captain Britain thing came to a pretty grisly end, for Slaymaster. Brian Braddock resigned from being Captain Britain, and his sister Betsy took up the mantle of the good Captain Britain. Slaymaster set a trap for Cap, expecting it to be Brian, but was a tad surprised when Betsy turns up. Slaymaster got Brian's attention by ripping out Betsy's eye's, the sort of nasty little thing an Arche-enemy does.
As you would expect Brian wa a little bit annoyed at what Slaymaster had done to his sister, and lost his temper, and killed Slaymaster with a big rock.
So no more Slaymaster, no more Arch-enemy!
But never fear Slaymaster has returned, granted he's not the original one, but someone called Jasper Bateman, a mercenary who was obsessed with Slaymaster's exploits. This episode happened in Deadpool team-up #893 in 2010.
Slaymaster was defeated by Captain Britain, and Deadpool, but I'm hoping that's not the last we see of him. Granted it's not the original one, but he'll do.
So come on Alan Davis, or Paul Cornell, please re-invent this rivalry between the two. Slaymaster and Captain Britain need to lock horns again, but hopefully written better than the team-up issue, and Alan Davis would be my first choice, only he can draw Captain Britain, how Captain Britain should look.