Warrabout Accchhhhhrrrrington Stanley?It was off the top of my head, but now you're asking:
Man United
Man City
Liverpool
Everton
Leeds
Blackburn
6 bigger clubs than Burnley with more success in recent years.
Then you have Huddersfield, Bradford, Bolton and Preston who are on a similar level to Burnley but still close enough to bleed some support if there are family connections or they are in the premier league while Burnley are struggling.