I think this is a dialect thing. I just googled Cheddar Gorge, and it comes up with pictures of what I would call a canyon, in England. Or, it could be a deep cut valley, with high cliffs on each side, but wider than a canyon. It probably depends on where you are. I'd consider a gulch a smaller version, similar to a wash (in Airzona, which is a place where water runs when it rains hard enough), an arroyo (in other parts of the Southwestern US), or a gully. They all look the same from the top.
I've been to the Royal Gorge bridge in Colorado many times.. quite a site... just so you can see one of our "gorges"... (open in a new tab or window so you don't lose your place here.)