The proposals are contained in a House of Lords amendment to the Health and Social Care Bill tabled by Baroness Finlay of Llandaff, a professor of palliative medicine.
They will be debated in the Lords next week, though there is understood to be widespread support both in the Lords and in the Commons for the changes to be made legal.
Lady Finlay said she was optimistic about the likely success of the amendment because it would benefit both parents and the NHS alike.
‘No greater nightmare for a parent’
She said there could be “no greater nightmare for a parent” than having to fight the NHS in court over the treatment of a critically ill or dying child.
It can cause “a terrible conflict” in which the parents’ “energy is taken up in fighting as their trust in the clinical team responsible for their child’s care haemorrhages away”.
She said: “For the clinicians, their energy is diverted into a legal case, taking their attention away both from the child and from other children in their care. My amendment requires that independent mediation, acceptable to both sides, is offered early when such conflicts arise.”
Parents would not automatically win the right for their children to be given novel treatments, but the amendment “aims to rebalance the dialogue towards resolution rather than a legal battle”, said Lady Finlay.
Ms Yates and Chris Gard, Charlie’s father, raised £1.3million to take their son to the US for treatment after he was diagnosed with encephalomyopathic mitochondrial DNA depletion syndrome, an exceptionally rare genetic condition.