They believe Zane Gbangbola was killed by hydrogen cyanide released from floodwater in their home, which they say came from a former landfill site.
The Chertsey family handed in a 16,000-signature petition.
The agency said it was working with police to investigate the matter.
Tests during the summer showed Zane died from carbon monoxide poisoning, but his parents, Kye Gbangbola and Nicole Lawler, dispute the findings.
Mr Gbangbola, 48, a company director who was left paralysed by the same incident, said: "We are starting to believe the causes behind his death are being swept under the carpet.
"It has now been nearly 10 months since he died and still we have had no cause of death, no date for an inquest and no assurances that our case is being taken seriously."
He said hydrogen cyanide had been found in the family's blood and had been identified in the house.
Mr Gbangbola said the family met Environment Secretary Liz Truss last week and she would be investigating the matter.
He said the family wanted answers and action to protect others, with further flooding expected this winter.
Supporters of the family include fashion designer Vivienne Westwood, who joined the march.
"It's so tragic what happened and there's no accountability for it even though the government are very well aware of what happened," she said.
"They've just turned away from it and left this man paralysed and his little boy dead."
A spokesman for the Environment Agency said: "This is a tragedy and our sincere sympathies are with the Gbangbola family.
"Along with other agencies we are working with Surrey Police who are investigating this matter."
Surrey Police said the force was trying to get answers for Zane's parents.
"The process is lengthy and we fully appreciate this is a frustrating and painful time for all concerned," it said in a statement.
The force said a pathologist had carried out tests after an initial inconclusive post-mortem examination and had given a result of carbon monoxide intoxication.
It said any evidence would be provided to the Surrey coroner for an inquest.
The parents of a seven-year-old Surrey boy who died during last winter's floods have marched with campaigners to the Environment Agency to demand a more rigorous investigation into his death.