Eight per cent also claimed that their cat or dog is healthy and doesn't need it, while six per cent said they simply could not afford it.
Steve Johnson, the head of pet insurance for Sainsbury's Finance, said that it was "alarming" that people disregarded cover due to such claims.
"Dogs and cats are just as likely to get ill and require treatment as we are but there's no NHS for them," he explained.
"Pet insurance really is essential if you don't want to get caught out by costly vet bills - the average claim for vet's fees is around £300 with one in every 26 trips to the vet costing over £1,000."
Previous research by Sainsbury's Bank found that the lifetime cost of owning a dog stands at around £9,000.
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