The exam would be at the end of medical school, before the MRCP or MRCGP.
Chris McManus, professor of psychology and medical education at University College London, found that medical schools leave their stamp on a student's postgraduate performance, irrespective of academic ability.
MRCP candidates from Liverpool and Dundee were most likely to fail, while those from Oxbridge and Newcastle were most likely to succeed.
A new MRCGP league table ranks medical schools in a very similar order to the MRCP one.
Professor McManus lays the blame on 'medical-school related factors'.
'Graduates from different medical schools perform markedly differently in terms of their knowledge and clinical and communication skills,' he said. 'There seems to be a strong case for a national exam,' he added.
Liverpool shares the bottom end of the MRCGP league table of 23 medical schools with Manchester and King's College, London.
Newcastle and Oxbridge are second and third, with Nottingham first in the MRCGP league. Dundee was placed 18th.
The league table, which was prepared for the RCGP's examination board, shows that pass rates among 3,787 graduates in 2003/6 echo medical schools' achievements as long ago as 1988 to 1991, when Oxford topped the table and Liverpool and Dundee took two of the bottom four places.
Dr Richard Wakeford, the VTS course organiser and Cambridge University assessment expert who compiled the MRCGP tables, agreed that the system needs to change.
The tables show how pass rates for the MRCGP have plunged in some deanery areas. Big changes 'ought to be studied carefully to see what general lessons can be learned', Dr Wakeford said.
The abstract raises the possibility of 'differences between medical schools in teaching focus, content and approaches'.
It adds: 'Exploration of causal mechanisms would be enhanced by results from a national medical qualifying exam.'
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