Three other people have been treated in hospital.
Child heart operations to permanently stop
A review is recommending child heart surgery at the John Radcliffe Hospital in Oxford stops permanently.
The change would be part of reducing the number of units performing children's heart surgery in England from 11 to six or seven.
Experts say this will lead to safer services and will ensure doctors and surgeons are able to maintain their expertise.
The idea of cutting the number of units was first raised more than a decade ago following the Bristol baby heart scandal when children died needlessly.
An inquiry, led by Professor Sir Ian Kennedy, said children should have heart surgery in fewer centres, which would be more specialist. A follow-up report published by Sir Ian on Wednesday says not all 11 centres would be able to meet new clinical standards.
It is thought larger centres are better placed to recruit new surgeons and plan for future surgery. But opponents say the changes mean parents will have to travel further to visit their very sick children and some units under threat are performing well.
The 11 units under review are:
Alder Hey Children's Hospital, Liverpool; Birmingham Children's Hospital; Bristol Royal Hospital for Children; Evelina Children's Hospital, London; Freeman Hospital, Newcastle; Glenfield Hospital, Leicester; Great Ormond Street Hospital for Children, London; Leeds General Infirmary; Oxford John Radcliffe Hospital; Royal Brompton Hospital, London; Southampton General Hospital.
What are the options?
The review has come forward with four options . All of these involve stopping child cardiac surgery at the John Radcliffe, and all but one suggest operations should also be stopped in Southampton.
The John Radcliffe has already stopped its operations following several deaths last year, with patients currently traveling to Southampton for surgery. Now both hospitals are getting together to come up with another plan, which could see local services kept in both cities, with more complex procedures carried out in Southampton.
Sir Jonathan Michael, Chief Executive of the Oxford Radcliffe hospitals NHS Trust said:
"A partnership between Oxford and Southampton will ensure that children and families in the areas we serve receive the best treatment available. We believe that it is in the best interests of patients that services are preserved as locally as possible and it is important to remember that surgery is only one part of the treatment of children who often have complex needs.
"The networking arrangement that is working so successfully with Southampton is a innovative opportunity to provide excellent care in a way that fulfils the aims of the Safe and Sustainable review while preserving the wishes of many families that they access the majority of the care for their children as close to home as possible."
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