If you look at how many film deals BBC have they have a massive catalogue of films they never show.
I remember watching Twins on BBC One years ago (around 2005/2006) for the first time but that is now on ITV.
I doubt Sky will want to re-new the contract the novelty has worn off for them. They won't want them any more.
The BBC have all of BBC Films and DreamWorks Animation. As well as selected titles from Disney, DreamWorks* and indie companies like Sony Pictures Classics and Pathe.
*They have everything DreamWorks have the rights for, but a lot of DW's catalogue are co-productions for which somebody else has the rights
A lot of that does get some airing, and even Channel 4 who have a massive library (Fox, Paramount, Studiocanal, Relativity Media, Momentum, Film4, Entertainment One, MGM and selected films from Sony Pictures, Disney and EFD) repeat themselves.