It wasn't Comic Book was it? Had an early morning slot at the weekend (around 6am) where the Channel 4 Daily ran during the week.
Nope, Comic Book used classic American cartoons, rather than international animation. I think you're thinking of Fourmations, but I'm not certain.
It's not Fourmations as those were shorts C4 fully funded themselves and generally self contained. These were international animations that C4 didn't fund - just had rights to show.
I wonder if it was for their "Animation Week" in 1994 - What I remember is the show was *long* - there was an animated host for the duration, it went into history of animation including US animation like Windsor McCay's Gertie the Dinosaur but also featured Russian, Croatian, Japanese and indie animation. It wasn't any of the full films, but you would get clips and a truncated "full" short of each example.
It sounds like the 1998-9 series "Dope Sheet" but I know it wasn't that as the host absolutely wasn't CGI - they were 2D and the films picked ranged from kid friendly to quite questionable. It's possible it wasn't C4 at all, but it seemed an awful lot like the sort of thing only Channel 4 would put that much effort into.