Here is a table showing the number of consecutive seasons played in the Top Flight of English Football since winning promotion for the current Premier League clubs... please log in to view this image The total number of seasons spent in the Top Flight since 1888-89 can be found here: Seasons in the Top Flight of English Football by Clubs
Arsenal never won promotion to the Top Flight. Instead, they were "elected" to the First Division in 1919-20 and remain the only club never to have earned their place in the Top Flight on merit.