Justin Balcombe, a partner at accountancy firm KPMG, also warned that many households and businesses do not have enough insurance to cover losses.
He said: “The scale of the flooding over the last few weeks has seen communities across large sections of Yorkshire severely impacted.
“In 2007 when a similar pattern of flooding hit parts of the UK total insured claims were £3.2bn, however, we consider that the actual financial impact far exceeded this.
“We are assessing this month’s events across affected parts of the country through a number of economic lenses, resulting in an initial total cost estimate of £5-£5.8bn.”
Mr Balcombe, who is head of general insurance consulting, estimated that insured losses would be between £1bn and £1.5bn. Underinsured losses could reach £1bn, he added.
Mr Balcombe said: “We believe that there is a serious level of under insurance and would estimate this economic impact to be as significant as the insured event.”
Many households are still feeling the effects of the recession and have reduced insurance premium spend and coverage, he added.
Mr Balcombe said companies that have been impacted by flooding may take longer to return to pre-loss profitability while their insurance coverage may not extend beyond a 12-month business interruption period.
He predicted that the cost to local authorities of bringing communities back to normal could reach £750m due to the scale of flooding and level of infrastructure damage, excluding any new investment in reinforcing flood defences.
Mr Balcombe said the Government will face calls to step in and help fund knock-on effects to public transport, utilities and social services as well as extra support to rural communities and those on low income without insurance.
He said repairing and replacing flood defences will cost £2bn, which includes the impact on next year’s insurance premiums in renewal.
Meanwhile, insurance companies have visited areas struck by floods to advise people on how to make claims.
Teams are on the ground in Yorkshire and Lancashire to meet customers who have been flooded and help them in the recovery process once the waters subside. 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.”