Riots broke out on Saturday night following a peaceful protest in Tottenham over the police shooting of local man Mark Duggan.
Unrest spread across the capital to Peckham, Wood Green, Enfield, and Hackney, and around the country to Birmingham, Bristol, Liverpool and Nottingham on Sunday and Monday.
Nick Starling, director of general insurance and health at the ABI, urged people whose property has been damaged by the riots to contact their insurers straight away.
“Insurers are working as quickly as they can to deal with claims. However, access to dangerous buildings which are also crime scenes is a serious issue,” he said.
“It is too early for us to have an accurate picture of total costs, especially business interruption costs, but insurers are expecting significant losses, of at least tens of millions.”
Mohammad Khan, partner at PwC, said the rioting may have deeper implications for insurers other than the immediate payout costs.
“There may be some specific increases in premium for the worst affected areas but, for customers nationwide,” he said.
However, he added competition between insurers may mitigate this.