I'm a fan of that particular show, despite being a motorcyclist.
I watched the episode in question & DID NOT notice anything amiss at the time - they were talking about the bridge, right

Yeah, we know it's all heavily scripted etc & we know that JC has become, to a degree anyway, a victim of his own success.
Part of the shows' appeal is that they push things as hard as they dare (for the Beeb, anyway!) but to sue over this is just insane.
In my books, "Slope" is no more of a racial insult than:
Brit
Yank
Jock
Paddy
Clog
Kraut
Frog
Chink
Dago
*add your own*
and this silly slapper should be told to SHUT THE FUCK UP & leave our national treasures alone.