Morgan played international rugby for Wales and in 1908 was selected to join Arthur Harding's Anglo-Welsh tour of New Zealand and Australia.
It was while representing Cardiff, that Morgan was selected for the Anglo-Welsh team to tour Australia and New Zealand with his brother Teddy.
Joining Morgan at half back were two other Welsh players, James "Tuan" Jones and, moved from threequarters, Reggie Gibbs.
In a home game played at the Cardiff Arms Park, Morgan was brought into the Welsh team to face Scotland as part of the Five Nations Championship as a replacement for Dicky Owen.
After his rugby career for Cardiff came to an end, Morgan would often turn out for French team Stade Bordelais, where he was nicknamed "Billy Bordeaux".