NFU Mutual, which supports rural communities, has also activated its emergency plans to support people.
Rob Townend, UK claims director for Aviva, said: "Property damage as a result of flooding or storms is one of the most traumatic events that a homeowner and business can suffer.
"This trauma places huge responsibilities on us, the insurance industry. We can't stop the weather, but we can work tirelessly to support our customers affected by the events brought by this horrendous storm."
Customers with Aviva are covered for flood and storm damage, Mr Townend said, and the company can also make emergency payments to help people pay for items such as baby food, nappies and clothes.
He said: "Any damage caused to property and belongings will be covered and if customers have to move out of their home, because it is uninhabitable, the cost of alternative accommodation is also paid for - and we can make arrangements for pets, too.
"Once we have assessed any damage we will install drying equipment for those properties that need it and for those people who can't remain in their homes we will arrange alternative accommodation as soon as possible."
People who have been flooded are advised to contact their insurer as soon as possible and to make a list and take pictures of any items that have been damaged to help speed up a claim.
Matthew Scott, chief claims manager from NFU Mutual, said: "Based on what we are hearing from our network of offices across the UK, the flooding across many parts of northern England and north west Wales could be the worst for several years.
"As a result of this, we have activated our emergency plan and our staff and agents are working hard over the Christmas period to support their local communities.
"Having a local presence means we've been able to react quickly and provide immediate assistance to families and businesses in all of the areas worst affected by Storm Eva.
"This is a particularly cruel weekend for anyone to be affected by a flood and our first priority is to help get our policyholders and their families back into their homes and workplaces as quickly as possible.
"We have teams of loss adjusters ready to assess the damage and arrange repairs as soon as the flood waters have subsided."
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