Footie was most certainly kicking around (ahem, excuse me

) in Tolkien's day; many of our most venerable teams such as Preston North End, Bolton Wanderers and Sheffield United and Wednesday had been in existence for some time, and footie certainly was attracting enormous crowds in the North of England and in all working class areas. During the 1930's the sorts of crowds that would flock to matches put today's crowds to shame; of course there were no seats, and little security so people would crowd in to watch.
Also football stretches back to the medieval period in the UK, when matches would be played in the streets with very few rules and a lot of drunken rowdiness. Teams would often consist of one side of a town versus the other and some towns still revive these rowdy scenes; they still have this 'game' at Ashbourne in Derbyshire, and it resembles a huge riot.
Here's a link to the great tradition of
Medieval Footie
It was the public schools who eventually came up with actual rules, which also resulted in the division between Rugby and Footie. Maybe this resulted in some of the class divisions between fans of Footie and Rugby - though Rugby League is still very much a working class sport, hugely popular in Northern towns like Wigan, St Helens, Bradford, Huddersfield etc. Rugby Union is more characteristic of public schools and towns like Bath. I presume Tolkien played Rugby Union rather than Rugby League? It's been known for fans of Rugby Union to dislike Footie.
Funnily enough, though many of his fans are probably not huge sports fans (though a lot are, before SpM, Esty and Phantom jump down my neck

), Tolkien was pretty good at sports, and he fell in with the 'hearty' set of his time who disliked aesthetes, so might we expect to see sport in his work?