Bille August's The Best Intentions, Peter Greenaway's Prospero's Books and Terence Davies' The Neon Bible would be my choices from the Film4 catalog. Sadly, none of them are specified in the Variety article. The article also says that Twilight Time are attempting to get some French titles, which is exciting to say the least.
Going by the age of some of the titles already announced, I am guessing that whatever Twilight will be releasing from Film4 will be mostly '90's vintage, since anything more recent is likely still tied up in U.S. distribution licenses. I would dearly love a Blu-Ray of CROUPIER, especially with the Hodges commentary taped for the UK release, but I'm betting it's still held as an asset in The Shooting Gallery's library.
THE CRYING GAME is likely Miramax's in perpetuity for the U.S.; when it became a hit, they increased their ownership stake in the film.I would guess that both SECRETS AND LIES and CAREER GIRLS will eventually come out through Criterion, since they've already released other Mike Leigh films, and through either their relationship with Focus Features (provided they still have U.S. rights), or through their relationship with Film 4 (if the old October deal has run out).