I know Notts County are the oldest. When the Football League was founded in 1888, the twelve teams were:
Accrington, Aston Villa , Blackburn Rovers , Bolton (5)Burnley, Derby County , Everton, Notts County, Preston North End, Stoke, West Bromwich Albion and Wolverhampton Wanderers.
My guess is Preston North End bit it could be any of them.