Professor Nigel Heaton, head of the transplant unit at King's College Hospital in London, transplanted part of the liver into a boy from one of the Gulf states.
Other doctors complained that a child on the NHS organ waiting list should have been given priority. National guidelines state that, because of the acute shortage of donor organs in Britain, livers must be offered to all other NHS centres before they can be given to a patient from outside the European Union.
There are about 400 NHS patients on the liver transplant waiting list - 20 per cent of whom will die before a suitable organ can be found.
The incident sparked fury among surgeons at St James's University Hospital in Leeds, which first received the liver from a 40-year-old donor. After instructions from UK Transplant, which co-ordinates NHS transplant services, the Leeds surgeons sent the liver to King's for a 'super-urgent' adult NHS patient on the understanding that it was to be used solely for that person.
St James's only learned the following day that Prof Heaton had split the liver into two when a member of staff from King's contacted them, Daily Mail reports.
Prof Heaton had used the larger right portion for an adult NHS patient and transplanted the left lobe into a seven-year-old boy who had rejected an earlier liver and was seriously ill. He later died.
A senior medical source said: 'This was clearly a violation of procedure. It should have been offered back to every other hospital within the NHS and then throughout Europe before going to a non-NHS recipient.
'There is no process for it to go to a non-entitled patient on compassionate grounds. It just doesn't happen.'
David Mayer, chairman of UK Transplant's Liver Advisory Group, said the Leeds doctors had been extremely concerned because they had a sick child, an NHS patient, who could have benefited if they had known the liver was to be split. He added: 'If we were to provide livers for the world from the UK, then UK patients would be enormously disadvantaged.'
The procedure of splitting livers has been developed in recent years to counter the shortage of donor organs, particularly for children. Because livers are able to regenerate relatively quickly, two patients, usually an adult and a child, can be treated with one organ.
Normally, livers from donors aged over 40 are considered too old to split, so UK Transplant had not expected this to happen in this case.
In a statement, King's said they had applied to have the Gulf state's child considered for priority liver transplantation on compassionate grounds and that there had been no objections.
They said that the investigating panel had found that guidelines had been breached and that it had recommended that King's review its practices and ensure all staff were aware of transplant guidelines.
A King's hospital spokesman confirmed that Prof Heaton had been paid for the original transplant on the private patient - which had been rejected - but had received no further fee for the second operation.
Daily Mail also reported that the King's has given livers from UK donors to 22 private patients from Kuwait and the United Arab Emirates in the past five years. The hospital has made more than Ģ4million from performing transplants on overseas patients in that time, the newspaper said.