Why Bristol City will Be a Premier League Club in the Future. Bristol City’s highest ever finish was way back in 1906-07 season, when they finished title runners up and they have not appeared in the English top flight since the 1979-80 season. They have never won the FA Cup (they were runners up in the 1908-09 season), or League Cup. Their last cup success was back in 2014-15 when they won the Football League Trophy. Despite gaining promotions as either league winners or runners-up in the lower tiers of the football pyramid, they have never managed to regain their place among the English elite. Although history doesn’t make a convincing argument for why Bristol City are a future Premier League club, when we look at their recent off-field activity it is a different story.