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.)
It's interesting that some native English speakers didn't know the word "gorge."
Perhaps the word is falling out of use. or perhaps it's because gorges aren't found in all parts of the English-speaking world.
The Finger Lakes region of New York is known for its beautiful gorges that were carved out by glaciers. I've seen the phrase "Ithaca is gorges" -- a play on the word "gorgeous" -- used in promoting the city that is home to Cornell University.