The firm said its hand had been forced by a similar rise in claim costs over the past two years, during which time insurance rates had remained static.
Norwich Union said claims for personal injuries had been the main reason for the rise in its costs. Insurance for riskier customers, such as young men, will rise by up to 40%.
David Ross of the Norwich Union said: "I think we'll find that most insurance companies will follow our lead. We're the largest insurer in the country and one of the largest motor insurers," he said.
"There is an expectation amongst various commentators in the sector that motor premiums will need to rise to reflect the increase in claims costs, particularly from the more litigious society that we find ourselves living in," added Ross.