League Cup runner-up cannot take the UEFA Cup spot if winners already got Champ League spot [e.g. 2005-2006 Final Man Utd 4-0 Wigan, but Wigan didn't get UEFA Cup spot even Man Utd got Champ League spot]
however FA Cup runner-up can [like 2005-2006 West Ham].
however if both finalists of FA Cup already taken Champ League spot [like 2006-2007 Final Chelsea 1-0 Man Utd], then the UEFA Cup spot will be gifted to next best-position league team.