The slide in fish ownership also came in the wake of a crackdown on funfair or fete stallholders handing out goldfish as prizes to children under 16.
In the past they were widely distributed this way, but now those who do can now be jailed for up to a year under animal protection laws. The same sentence would apply to pet shop keepers who sell animals to under-16s unless an adult is present.
Emma Milne, a TV vet, said: "I'm sure the rise of social media has had an impact on pets from all angles and may well have affected fish numbers while conversely hiking the popularity of other pets.
"Also goldfish used to be readily accessible pets when I was a kid because they were in bags to be won at every fair. This was poor for welfare and changed for the better but I do think it contributed massively to impulse taking on of fish. They're not in the public eye now and we have the double whammy of social media."
Overall pet ownership has tumbled by seven percentage points in five years, the data showed, with just over half (56 per cent) of UK households now containing a pet, down from 63 per cent in 2012. Fish were the pet whose popularity is falling the fastest.