Cellular network

I live in the UK and have an iphone. When I was in the USA last year I bought an Apple watch with GPS and cellular. I am currently on an iphone plan with 3 network which is not compatible with the watch so I am looking at changing my iphone plan to one of the carriers that it says it will work with eg EE, 02 and Vodaphone. However, when I looked up the model number of the watch, the UK isn't listed as being a supported network. Does that mean that the watch won't be compatible even if I change mobile phone network providers?