Ministers have ordered an inquiry into NHS organ transplant arrangements for EU residents.
It is thought nearly 800 transplants have been carried out by the NHS on non-UK patients over the past decade.
This has prompted a row over whether transplant centres were right to grant these procedures.
The review will be headed by Elisabeth Buggins, who last year led the Organ Donation Taskforce into the issue of presumed consent.
The aim of the review is to clarify the situation over the rights of EU citizens to get NHS transplants.
Figures released in January showed that 795 organ and tissue transplants were performed on non-UK patients over the past 10 years.
Patients will be pleased that the Government finally seems to be waking up to the scale of the problem, but ministers have known that this has been happening for 10 years
Stephen O’Brien, shadow health minister
They included 674 liver, 47 kidney and 57 cornea operations.
However, over this period a total of 140 organs were imported into the UK for transplant and there are thought to be a number of UK residents who have gone abroad for treatment although the exact figures are not known.
European law requires that NHS hospitals give EU patients the same access to services as UK patients.
But it is unclear how exactly that relates to transplants.