The study found six out of 10 parents with children under 18 years had no protection cover or financial provision in place to support their own or their child’s medical bills, as well as any time off work to look after a sick child.
One fifth of parents stated they would have to rely on savings at a time when interest rates on savings are at rock bottom.
When parents were asked how much they would be prepared to pay for a critical illness policy which covered themselves and their children, 15% said they would be prepared to spend £5 a month.
Some 17% would spend up to £10 each month and a further 10% would commit to a monthly premium of £20.
Andy Milburn, head of marketing at Ageas Protect, said: “It’s clear that parents are willing to pay to protect themselves and their children for a reasonable monthly amount.
“Starting off with a small amount of critical illness cover could be the perfect solution to help educate not only parents but consumers up and down the country.
“Critical illness cover can be taken out for the same monthly outlay as a pet insurance policy, and will provide a vital support at a time of need.”