As every self-respecting Pub Quizzer knows, the largest city in England without a recognised club in the Football League Pyramid is Wakefield, West Yorkshire. They have Wakefield Trinity Wildcats Rugby League Club, of course, but their football club - Wakefield FC - folded in 2014. More info on Wikipedia if you want it:
https://en.wikipedia.org/wiki/Wakefield_F.C.
Wakefield FC were previously known as Emley AFC - not to be confused with the current club AFC Emley, which was founded in 2005 (9 years before Wakefield FC folded). Other local rivals will include Leeds United, Huddersfield Town, Bradford City and the re-formed Halifax Town AFC. I'm a blast at parties, honest!
Although they've folded, they will still be included within the FM database. To reactivate them, you'll need the Football Manager Editor programme that you can acquire for FREE through Steam once you've bought the game. You can edit their details, too, if you want to differentiate your club from that previous one. Their ID is 4002015. If you reinstate them into one of the non-league divisions, remember to remove another club from the same division to accommodate them; they were in the Northern Premier League Division One North in 2013/14. Probably teaching you to suck eggs there, but this info might be useful for others!
I have the club badge and kits for that previous club within my Graphics folder:
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If Wakefield FC doesn't float your boat, you are welcome to come over to my Custom Logo Creation Thread to get a new badge for the custom team of your choice - this link will take you to pg.61 where I posted my 'Best of...' collection, but browse on to the end to see those I have done more recently; if I do say so myself, I think I'm getting better at them!:
http://www.fm-base.co.uk/forum/club...-rocheybs-custom-logo-creation-thread-61.html