Children's heart surgery at Oxford's John Radcliffe Hospital should stop, a national review of paediatric heart centres in England has said.
Surgery was suspended there in March after four children operated on by the same surgeon died in three months.
The review will recommend that three or four other paediatric heart units out of 11 in England also stop surgery.
The aim is to improve the safety of heart operations by having fewer, more specialised centres.
Children's heart surgery at the John Radcliffe has been under the spotlight since it emerged that four children died there between last December and February of this year.
An inquiry found that the deaths were not due to errors of judgement, but that the surgeon had not been given appropriate supervision.
It criticised the hospital trust for "serious shortcomings", in the way it had taken on more cases to try to avoid closure of the paediatric unit.
Paediatric cardiac surgery at the hospital remains suspended.
An expert group has been reviewing the work of the 11 centres across England which conduct this type of specialist surgery.
The review was launched in response to the 1990s Bristol heart babies scandal, when children having heart surgery died unnecessarily.
Its full recommendations are due early next year, but it is likely to say that the four or five smallest centres should stop carrying out operations.
This number would include the John Radcliffe cardiac centre, which it has already ruled is too small, and lacks the expertise to offer a good service to patients.
It will recommend that the Oxford children's cardiac unit stops doing surgery, but continues to offer diagnosis and pre- and post-operation care.
Leslie Hamilton, former president of the Society for Cardiothoracic Surgery and a review member, said the decision was aimed at improving the safety of heart operations.
"The NHS needs to ensure the very best outcomes for children," he said. "Children's heart surgery is complex and must be performed by highly skilled specialist surgical teams.
"Pooling surgical expertise into fewer, larger centres is in the best interests of children and their families."
The recommendation to close the Oxford surgical unit will be the subject of a public consultation. However, it is highly unlikely that children's operations there will now resume.
The John Radcliffe hospital described the news as disappointing for patients, their families and staff. But Director of Planning, Andrew Stephens, said it was not entirely surprising. "Oxford is one of the smallest centres," he said, "and the main thrust of the review is that there should be fewer, larger paediatric cardiac centres in the future."