Mr Sullivan , one of only 25 members to be inducted into the sport’s hall of fame, died on Tuesday, aged 82, following a long illness.
He began his playing career with Shaw Cross amateur club and is recognised as one of the greatest players to come out of the Heavy Woollen district.
Shaw Cross Sharks ARLFC secretary Douglas Hird said: “He was a fine athlete from the day he came to play at Shaw Cross. He had speed, agility and was a tremendous competitor.
“Mick Sullivan was one of the finest players Rugby League has seen and we are so proud that he started here at Shaw Cross.”
Mr Sullivan went on to sign for Huddersfield in 1952 and was later involved in record-breaking transfers to Wigan for £9,500 in 1957 and then to rivals St Helens for £11,000.
He also played a spell with York before ending his career as player-coach with hometown club Dewsbury.
Dewsbury Rams paid tribute to the star on social media.
A statement read: “We are sorry to learn of the death of RL legend Mick Sullivan. He was player-coach at Dewsbury between 1965-66 with 40 appearances.”
Mick set the record for the most caps with Great Britain - 46 - a record later equalled by Garry Schofield, but never beaten.
And in his national career, the winger scored an unsurpassed 41 tries, helped GB win the World Cup trophy in 1954 and 1960 and scored a hat-trick of tries in the deciding 1958 Ashes test in Sydney.
RFL chief executive Nigel Wood said: “Mick Sullivan was one of the greatest Rugby League players to ever play the game.
“A World Cup winner at just twenty years old, Great Britain’s record try scorer and joint most capped player, he was a legend of the game and was rightly inducted into the Rugby League Hall of Fame in 2013.
“The RFL would like to offer their sincere condolences to his family and friends at this difficult time.”