Lord De Ramsey was criticised after the agency admitted that its reaction to the disaster, which left five people dead and thousands more homeless, "fell short of public expectations".
After the report was published yesterday, five MPs from Northamptonshire, where two people died and 2,500 homes were left under several feet of polluted water, said the chairman should be made accountable for the agency's failure to issue effective warnings and for bad co-ordination with local emergency services.
The cost of the floods, which deluged thousands of square miles of central England and Wales, has been estimated at between pounds 350m and pounds 400m.
Tony Clarke, Labour MP for Northampton South, said: "It is clear that vast numbers of people were flooded because of the incompetence of the agency."
Mr Clarke said: "We are now several months after the flood and he [Lord De Ramsey] still hasn't made any public comment or expressed any sympathy to the victims."
Lord De Ramsey, 56, was appointed chairman of the embryonic agency in 1995 by the Tory government. Last year, he was paid just over pounds 52,000 for a two-and-a-half-day week. An Environment Agency spokesman said its chairman had "no intention" of resigning.
The report levelled serious criticism at flood defences in Northampton, although it acknowledged that flooding could have occurred "irrespective of those deficiencies".
Sally Keeble, Labour MP for Northampton North, said: "The weaknesses exposed in this report mean no-one can have any confidence that he [Lord De Ramsey] can carry through the proposals."
Peter Bye, chairman of the independent review said that a "root and branch" overhaul of the agency's warning arrangements was urgently needed.
The report recommends:
Northants, Cambs, Bucks and parts of Beds: review of flood warning thresholds and a review of flood defences in some of the worst-hit towns. Trial of a siren system and the development of a local authority warden system in Northampton.
Midlands: review of flood warden systems; possible improvements to embankments, walls and other measures under flood alleviation schemes.
Oxfordshire: review of warning systems; review of river maintenance and develop flood defence for canals and rivers.
Wales: warning trigger levels to be lowered.