"Even the close bond and trust we had is quickly slipping away, due to the separation and confusion surrounding his care.''
Mrs Roberts requested a private audience with Mr Cameron or the Secretary of State for Health to relay her concerns.
"Mr Cameron, the power is in your hands to end this blatant miscarriage of justice and save my son today.''
Mrs Roberts fears radiotherapy will affect Neon's intelligence, shorten his life, put him at risk of having strokes and make him infertile.
He started radiotherapy after a High Court judge dismissed her case following medical evidence that Neon would die within three months if denied it.
Mrs Roberts took Neon and went into hiding, prompting a nationwide search. Since they were found Neon has been living with his father.
The judge in in the High Court case said he was worried Mrs Roberts' judgment had "gone awry'' over the seriousness of the threat to her son's life.
He had a cancerous brain tumour removed in October and a second operation to remove more cancerous cells last month.