Who actually coined the expression ‘my way or the highway’? No one knows, but it’s dollars to donuts that it was an American.
Many parts of the English speaking world use ‘road’ rather than ‘highway’, which is why this phrase works best in the USA.
The idiom was coined in the USA sometime around the 1970s.
The earliest use of it that I can find is found in the Tampa Bay News, August 1974:
In the article the board is accused of having a ‘my way or the highway’ attitude that resulted in ‘management of fear’ policies.
It may well be that the expression was in popular use before 1974 and that earlier examples of it will be found.