Quick thought would be for rugby to take a stronger hold in England after the 1895 split. Apologies if this sounds like a rugby league timeline, but it is a means to an end.
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1895 Rugby splits in two, when 22 northern English clubs break away to form the Northern Union. Over the next few years the new code will amend rules to create a different sport to rugby union.
1903 (POD) Despite overtures from the Football League, Manningham FC and Stockport County, two leading rugby league clubs, remain in the handling code. Many others follow their lead, including clubs such as Leeds based Holbeck, Bradford, North Shields and many minor clubs *
1903-1910 Rule changes create a rugby league game that is more attractive to spectators. Game expands to south Wales, Midlands and north east England. Australia and New Zealand take up the code. **
1910-1914 Rugby league consolidates in northern England, and continues to expand, whilst rugby union declines.
1914-1918 First World War. Regular fixtures suspended in all major sports. Soccer, as a major participant sport, feels impact of huge number of deaths more than competitor of rugby league.
1918-1922 Boom in spectator sport. Rugby league consolidates in England and Wales. Football remains strong in pockets of Merseyside, southern/eastern Manchester, Sheffield/Nottinghamshire and north London. Rugby remains strong in pockets of northern/western Manchester, West Yorkshire, Midlands and south Wales.
1922 onwards - English soccer weaker, rugby league stronger. Soccer clearly still the bigger game, but failed to capture the north of England, thus halting a production line of key players. Soccer thrives in Glasgow and other Scottish urban areas, with an excellent production line of players and becomes part of the national conciousness in a way that it failed to become national in England.
Scottish FA become more integrated and enthusiastic about international game than English counterparts.
Thoughts ???
* OTL both switched to soccer, along with many minor northern clubs. Better rugby league governance leads to clubs remaining in the sport. Manningham FC became Bradford City FC; Elland Road based Holbeck remain in rugby and their lack of demise causes Leeds City and Leeds Utd to never occur.
** Successful expansion leads to a thriving international scene by 1910.