No. Portsmouth would have been one but for one technicality - they didn't play in Europe the following season.
They were relegated from 20th place in 2009/10 and having reached the FA Cup final - which they lost to Chelsea who qualified for the Champions' League through winning the Premier League and thus not been able to take the UEFA Europa League place for the Cup win - they would have been eligible for the Europa League. But they had been placed in administration and lost 9pt - UEFA barred the club from competing in European competition and gave the place to Liverpool (the next highest league team) instead.