Did fish finger sandwiches ever go out of fashion? Hmmm, yes, maybe. I guess it depends on the definition of 'fashion'. Perhaps something's 'in fashion' when fashionable people take to it. Doesn't mean, of course, that it wasn't popular - just not popular with a certain group of people.
I'm remembering the scene in 'Happy Valley', where Sarah Lancaster's character meets the factory boss man in a cafe. She orders a fish finger sandwich and he, as if remembering how delightful they are, orders one too - with not a hipster in sight.