Sharon Hodgson, Labour's shadow children's minister, said David Cameron had created a "childcare crisis".
She said: "On his watch, we've seen costs spiral, support for families cut back and over 400 children's centres close."
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The film had formed part of a commemoration to the Choucair family, three generations of whom died in the fire.
John Nolan, who was found with cigarettes and two lighters, suffered burns on 65% of his body after being alight for around six minutes.
Known as Pily she died in January, seven months after the disaster, having suffered a stroke.