Charlie Gard's parents, whose campaign to save their terminally ill baby spread around the world last year, have called for a change in the law to give parents more control over the care of their sick children.

Chris Gard and Connie Yates said they had watched Alfie Evans' case with a 'heavy heart' and said it is 'impossible to understand the pain' parents Tom Evans and Kate James are going through.

They joined calls for a change in a law that currently demands courts take the child's 'best interests' as the 'gold standard' rather than the parents' wishes when ruling on how terminally ill children should be treated.

Cases such as Charlie Gard's and Alfie Evans' are judged on what is best for the patient's welfare, rather than giving priority to what the parents think.

Ruling in the Charlie Gard case, Lord Justice McFarlane said: 'The sole principle is that the best interests of the child must prevail and that must apply even to cases where parents, for the best of motives, hold on to some alternative view.'

Charlie Gard went on to die on July 28 last year and his parents have now launched a campaign to change the law.

'When we were fighting for our son, Charlie Gard, to be given a chance to try a treatment that could have improved his quality of life, we realised that cases like these would keep happening until the law was changed,' they said in a statement on Friday. 'Tragically, this has proven to be true.'

Alfie Evans' parents have been battling to take the 23-month-old to Rome and treated in the Vatican-linked Bambino Gesu hospital. A military grade helicopter was on stand by to fly him to Rome at the request of the pope, a court heard this week. But after a series of legal battles judges consistently ruled it was not in Alfie's best interest to travel and instead he should have life support removed and be treated with palliative care in Alder Hey hospital in Liverpool.

The case bears striking similarities to the Charlie Gard case and Chris Gard and Connie Yates said they were working with doctors, lawyers and politicians to 'propose a law that will prevent parents experiencing painful and prolonged conflicts with medical professionals'.

'This involves addressing problems around the "best interests" test as well as creating a platform for transparency and openness so that cases like these can be dealt with before they ever reach the courts,' they said in a statement.

'Once cases are public it is difficult for people to be fully aware of the complexities and this often leads to ill-informed judgements on both sides and creates unnecessary conflicts.

'We want to do something that is better for everybody – hospitals, healthcare professionals, families with sick children, the NHS, and the reputation of our own government,' they added.

It comes after independent MEP Steven Woolfe launched a similar campaign for 'Alfie's law' to give parents a bigger say in their child's treatment.

'The cases of Charlie Gard, Aysha King, and now Alfie Evans, show a dangerous trend of public bodies depriving parents and families of the right to make decisions they believe are in the best interests of their children,' he said launching the campaign outside parliament on Thursday.

'Parents' rights should neither be ignored nor dismissed as irrelevant by hospitals and courts, who believe they know best and have the power, money and resources to overwhelm families who simply want to save their child,' he added.

'Now is the time to act. We cannot have another baby, another family, have to go through the struggle and torment the Evans family have. It's time for Alfie's Law.'

Charlie Gard's parents appeared to ask Woolfe to abandon his campaign and join them as they said: 'We would ask those pushing for law change to take account of the careful work already done, and join us as we continue to push for a solution that is best for all involved.'