They say their son died from toxic hydrogen cyanide gas from a former tip near their Chertsey home and the petrol pump was not used.
They have accessed public health documents that stated firefighters found hydrogen cyanide in their home, but no carbon monoxide.
The latest development comes after a meeting on Wednesday between Zane’s parents, Kye Gbangbola and Nicole Lawler, Mr Chalk and Labour MP Richard Burgon, who is a long-term supporter of the family’s campaign.
The couple have repeatedly called for an independent inquiry but were previously told to apply for a fresh inquest.
Three Sussex councils have already backed Zane's Law, Lewes, Brighton & Hove and Adur.
This week, the BBC revealed a landfill experiment took place near Zane's home in the 1960s, with continuing questions about what waste went into the ground.
'Heartfelt sympathies'Mr Burgon said: "Zane’s parents have been fighting for justice for over a decade. It should not drag on any longer.
"I call on the government to immediately grant the Independent Panel Inquiry. That’s the way we can ensure that justice is done."
A Ministry of Justice spokeswoman said: "This was a tragic incident and our heartfelt sympathies remain with the family of Zane Gbangbola.
"The Lord Chancellor will raise their call for an independent public inquiry with the Secretary of State for Environment, Food and Rural Affairs."
The department also confirmed that the Lord Chancellor had committed to raising with the Prime Minister’s political advisers that the family would like to meet with the Prime Minister to discuss the case.
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