Sally Roberts has exclusively told ITV Daybreak that she is concerned that radiotherapy treatment could be damaging to her son Neon, by affecting his DNA.
She said there are "so many" other treatments that her son could be having instead.
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John Finucane, son of murdered solicitor Pat Finucane, only emerged as a leading Sinn Fein player last year.
Police officers found Allen hiding in bushes around an hour after the collision in Birmingham Road, Sutton Coldfield, last July.
A car on the driveway of Mr Adams’ property was significantly damaged in the blast.