I think an 18W US would be a 20-22 UK size. I always by my clothes in the US.. I have always assumed the W stood for Woman size (i.e. the politer version of plus size) but I may be wrong! As opposed to 18P which I have sometimes also bought, meaning Petite (i.e. shorter).
But I don't think W36, W,38, W40 and W42 mean the same thing as 18W. I've never seen the W at the start before, and also never seen something in a woman's dress size 42! So I expect that the sizing of that website is different.