Insurance against terror attacks must adapt to face up to the threats posed by so-called lone-wolf militants and the rise of cybercrime.

That's the view of Julian Enoizi of Pool Reinsurance Co., the U.K. government-linked body that backstops insurers against terror-related payouts. The spate of recent attacks in the nation's capital and the suicide bombing of a Manchester pop concert in May highlighted shortcomings in coverage that need to be addressed, he said.

"We need to close gaps such as business interruption that's not the result of physical damage and coverage of cyber terror, as well the low take-up among businesses outside of London," the Pool Re CEO said in a phone interview.