Zane Gbangbola died during floods in 2014 - his parents say he was killed by hydrogen cyanide washed out of the tip.
Now Spelthorne council's environment and sustainability committee has voted to take action at the site in Chertsey.
Committee chairman Ian Beardsmore said tests had not been carried out and it was "the right thing to do".
An inquest ruled Zane's death was an accident caused by carbon monoxide poisoning from a petrol pump brought in by his family to get rid of floodwater.
However, his parents Kye Gbangbola and Nicole Lawler always disputed the findings and said the pump was never in use.
Mr Gbangbola, who was paralysed in the incident, and Ms Lawler have now obtained Public Health England (PHE) papers backing their claims.
The papers, released to the family under a Freedom of Information request, include one document stating: "The house had three generators (1 x petrol, not operating, and 2 electric 1 of which was operating) in basement."
The document also said fire service testing detected no carbon monoxide.
A further note said firefighters confirmed "three hits" in the property for "hydrogen cyanide".
It said long-term exposure to the gas could cause cardiac arrest, adding: "The property has been flooded for the last 6-7 weeks with the family continuing to live in it - the [redaction] has been trying to pump out the basement and garden and the son has been in the flood water and garden."
Mr Gbangbola has told the BBC that his son never lived in the flooded areas of the home and only the basement was flooded. He said: "All habitable areas were dry and clean."
'Tests must be independent'Circulating the documents to the committee, Mr Beardsmore called for a report before 9 November stating how the authority would act in examining the site.
He said: "This is not ifs, buts or maybe, but how and when."
He said it needed to be decided whether action could be taken under emergency planning, contaminated land or health and safety legislation.
The committee voted unanimously in favour of action, but Mr Gbangbola said afterwards: "The tests must be comprehensive and done independently."
He also appealed to anyone with information to contact the BBC, adding: "Just do the right thing and tell the truth as you would expect others to do had your child been killed."
PHE said its staff, including the Porton Down-based Emergency Response Department, supported the 2013-14 flood response, and it later provided written evidence to the inquest.
It said Dr John Thompson from the PHE-commissioned National Poisons Information Service gave his expert opinion.
A spokesman for the coroner said: "An independent, full, frank and fearless inquest into the death of Zane Gbangbola was concluded in September 2016.
"The coroner's detailed explanation of his findings and conclusion has been available since the end of the inquest."
Mr Gbangbola said PHE were not present at the inquest, but "totally absent". He called for an explanation from the coroner.
Original BBC article by Tanya Gupta
AS IT EMERGES SPELTHORNE BOROUGH COUNCIL WANTS TO INVESTIGATE THE FORMER LANDFILL SITE IN CHERTSEY WHERE ZANE GBANGBOLA DIED, LUCY MAYER TALKS TO HIS MOTHER NICOLE.