Voice Actor Mel Blanc has played both roles.
In Robin Hood Daffy, Daffy Duck (voiced by Blanc) plays the role of Robin Hood. You might argue that Blanc is actually voicing Daffy Duck, but the character in the short is supposed to be the actual Robin Hood, not a duck merely acting like Robin Hood the way Bugs played a rabbit acting like the character without actually being the character in Rabbit Hood. The character on screen, voiced by Blanc, was supposed to be the actual Robin Hood (in satirical anthropomorphic duck form).
Blanc voiced King Arthur numerous times. He did so--again as Daffy, this time filling the role of Arthur--in Bugs Bunny in King Arthur's Court. Blanc also voiced an actual human version of King Arthur in Knighty Knight Bugs, in which Arthur assigns Bugs the task of retrieving the Singing Sword. He also played King Arthur in The Looney, Looney, Looney Bugs Bunny Movie and a 1963 Chuck Jones short called I was a Teenage Thumb.
Blanc was American of course, so it is possible that Connery is the only British actor to play both roles on screen.