The children's heart surgery unit at Oxford's John Radcliffe (JR) hospital could close as part of a national review of paediatric heart centres.
The JR unit is one of the smallest of 11 centres being assessed for their viability.
The NHS National Specialised Commissioning Group will recommend which centres should stop doing surgery, and which should be expanded.
The results of the study are expected to be published later this year.
Patients' groups have called for extra support for families facing long journeys if the JR unit is closed.
Professor Chris Ham, of the King's Fund charity which campaigns for improved medical services, said the primary issue is ensuring patients get the best care, even if they have to travel.
"I think most people would say that's a price worth paying, but support for patients and families making those journeys will be essential."
Cardiac surgeon David Barron, based at Birmingham Children's Hospital, said the centres would be reorganised to offer better care.
"These are very specialised services and they have to be delivered by teams of experienced professionals working together in centres of excellence.
"We know that you can't deliver that in smaller centres."