Isn't there wiki on this? I'm sure I saw one a while back about the history of football clubs.
There were other football clubs around besides Sheffield. The difference between Sheffield and other football clubs is that it was the first non-university football club. The other being Cambridge Football Club which was started in 1856 (may be 1855 but I don't have a page to hand with it

).
There were older football clubs first but they're not related to football. The most notable being St. Guys (or just Guys?) Hopsital. That's the first football club in the world, but they played rugby football so they're scrubbed from the record because it's not true football and Cambridge also since there were no definite records of their founding.
So, Sheffield were pretty much on their own for a while in terms of other non-university teams. They even had their own rule system and I know there's a wiki about this because the Sheffield and Cambridge rules were more or less the basis for the Football Association rules.
Suffice to say, there've been people kicking balls around on the ground for millenia.