A Farnborough resident who spoke to the BBC said the tornado in the town had caused "complete devastation".
Nick Starling, director of general insurance for the ABI, said: "While tornados in the UK are thankfully very rare, unexpected extreme weather incidents like this are exactly what insurance is here for."
He added: "Insurers will be doing everything possible to help policyholders who have suffered damage, and will be dealing with all claims as quickly as they can."
The ABI is the insurance industry's biggest trade association in the UK, with around 400 member companies.
Its moves to reassure the public come after it recently announced proposals for its members to offer discounts to customers who use environmentally friendly vehicles and install flood resilient measures on their homes.
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