Doctors warned Neon would be dead within months and he had already suffered as a result of delays from switching hospitals, missing appointments and his mother taking him into hiding.
Lawyers for the National Health Service now want Neon to receive radiotherapy, followed by chemotherapy, to give him a better chance of recovery.
Mrs Roberts, a 37-year-old New Zealander who has lived in England for 13 years, is concerned about the side-effects of the treatment which include possible stunting of growth and intelligence, as well as infertility.
The NHS also wants a court order for Mrs Roberts to hand over her son's passport - the implication being that she could flee with Neon as she did this month.
But in giving evidence, Mrs Roberts said the order was unnecessary because Neon did not have a current passport.
Her lawyer Ian Peddie, QC, asked whether she would take Neon to New Zealand. She denied being a flight risk.
"I would never take him away from his father ... I've lived here for 13 years, England is my home now."
Mrs Roberts also accepted a proposal that her former husband, Ben Roberts, should have custody of their son.
"As long as I can see my son every day and be part of his recovery."
Justice Bodey said he would deliver his ruling on whether radiation therapy was in Neon's best interests overnight (NZ time).
He said the "bottom line" of the case was balancing the disadvantages of radiation therapy against the improved survival rate for Neon.
"But you only suffer the disadvantages if you are alive," Justice Bodey said, in an indication of his thinking.
The hearing at the Royal Courts of Justice in London has provided a rare insight into the workings of a family legal dispute, which are normally shrouded in suppressions to protect the identities of those involved.
But reporting restrictions were lifted when the four-day disappearance of Mrs Roberts and Neon sparked a nationwide manhunt in Britain this month.
Neon was diagnosed with a medulloblastoma tumour, which doctors believed they had removed during a nine-hour operation in October. But Mrs Roberts refused to let her son receive radiotherapy following the first operation, and recent MRI scans picked up a growth of 1.5cm.
She has told the court she is not a "bonkers mother".
After failing in her bid this week to delay the second surgery, Mrs Roberts wanted more time to prepare her legal case in favour of alternative therapies.
Most of the therapies proposed in court yesterday were rejected by the paediatric oncologist, who can bereferred to only as Dr A, as "experimental".
None had been proven through clinical trials, he said. Dr A conceded there were negative side-effects of radiotherapy, but said these were outweighed by the greater chance of living.
Mrs Roberts was adamant that nothing she had heard from Dr A had alleviated her concerns.
But she was willing to support orthodox treatment if that was what the court ordered.
She also opposed the proposal from the NHS to appoint Neon's father - who wants his son to receive radiotherapy - as the sole decision-maker.
"I think that's very unfair. Neon is my son and I should be there for his treatment.
"I think it should be both of us (making decisions), equal say."
She was an active participant during the hearing, listening intently to Dr A's evidence, writing notes and whispering questions to her lawyer during his cross-examination.
Mrs Roberts denied accusations from the NHS that she prevented nursing staff from giving Neon anti-sickness medication after his operation.
• For the latest on this story go to nzherald.co.nz.
