I've only seen this show once or twice around 2006-2008 but been thinking about it for years because i cant remember the name or find anything on it. basically from what i can remember, the only characters i can remember was a man and a horse, i think the show was either claymation or some weird 2d animation that looked a little cgi like, the characters limbs were just thin black lines and i think they were either british or australian, i believe the man was blue and the horse was yellow? i could be wrong about the colours, i just remember them being weird colours. the show wasnt gumby btw but if anyone knows anything plz let me know thx! (also idk if this helps but im canadian so idrk about australian/british channels)
This probably isn't it but my first thought was A Town Called Panic... It's a stopmotion series featuring men and a horse character and it aired around the time you're describing, and some of the voice actors of the English dub were british. What's throwing me off is that "the characters limbs were just thin black lines"... they're made to look like toy figurines, so I don't think they fit that description.