It also warned that urgent action was needed to establish who is responsible for surface water flooding, which caused much of the damage last year.
Chief executive of the EA Paul Leinster said: "We believe that the Environment Agency in England should be given a strategic overview role for all types of flood risk - and when given clarity on this role and the role that local authorities will play, we can begin to advise on priorities for action."
An independent interim report in December said planning for flooding should have the same priority as terrorism or flu prevention.
Inquiry chairman Sir Michael Pitt also said the public should have been better prepared for last summer's floods which saw about 13 people killed and 44,600 homes and 7,100 businesses flooded, with the damage caused costing £3bn.
Sir Michael's final report is due at the end of this month.
Meanwhile the Environment Agency said it had:
• Inspected 8,500 km (5,300 miles) of defences, and spent £5m on repairing those damaged last summer
• Spent £125m on investigations and maintenance on main rivers, including CCTV surveys on waterways in Gloucester to check for and clear blockages
• Put in a £14m defence scheme in Nottingham to help protect more than 5,600 properties, and a £13.1m scheme to protect nearly 1,000 properties in Carlisle.
Key utilities such as electricity and water must put protecting their critical infrastructure higher on the list of priorities in the face of climate change, the agency said.
And Paul Bettison, chairman of the Local Government Association's environment board, said they should be given tough incentives to do so.
"There are glaring gaps in this country's readiness to cope with widespread and prolonged flooding," he said.
Laser maps like this one of Hull, with at-risk areas in green, could help combat floods
"Last summer's floods were no fluke, and we run the real risk of witnessing a repeat - or worse - unless urgent action is taken now.
"Councils should be allowed to start banging heads together so we can be better prepared to protect people and property."
But Institution of Civil Engineers director general Tom Foulkes said a spate of recent power station closures was to blame for putting pressure on energy companies' resources.
"It's all very well the EA telling utility companies they have to protect their critical infrastructure, but what we really need is to have the spare capacity that has been lost over the years built back into the system," he added.
A Department of Environment, Food and Rural Affairs spokesman said the government was working on the issue.
"We have already consulted on who should take the lead on urban drainage and how best we can clarify responsibilities so that we can improve how we tackle surface water flooding."
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