Jeremy Corbyn's party made the pledge in its manifesto, which was released on Thursday (November 21), among a number of cases that it has described as "historical injustices".
Within the 105-page manifesto, the party vowed to "consider a public inquiry in the case of Zane Gbangbola", as well as ensuring the "second phase of the Grenfell Inquiry has the confidence of all those affected, especially the bereaved families and survivors".
The Chertsey schoolboy died when he was consumed by toxic fumes at his flooded home in 2014 after the Thames burst its banks. His parents Kye Gbangbola and Nicole Lawler have been "fighting for justice" for their son ever since Surrey's senior coroner Richard Travers ruled his death as accidental following an inquest hearing in 2016.
Campaign group Truth About Zane posted a message of thanks on its Twitter page following the publication of the party's manifesto.
The Fire Brigades Union and trade unions have also thrown their support behind opening an inquiry into Zane's death, with shadow justice secretary Richard Burgon telling a Labour Party conference last month a Labour government would hold an independent panel inquiry "to finally get the truth about Zane".
"People shouldn't have to fight for justice, but in the society we live in, sadly, all too often they do," he said.