New guidance from the Academy of Medical Royal Colleges says every hospital patient should have a named doctor taking responsibility for their care.
The Government said it would introduce the measure as part of its response to the Mid Staffordshire NHS Foundation Trust public inquiry.
The "name above the bed" policy will ensure that patients and their relatives and carers will know which doctor is ultimately responsible for all aspects of their care, the AMRC said.
Around 40% of hospitals in England are understood to provide such details but health officials want to see the initiative rolled out across the board.
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Their warning depends on whether negotiations for a post-Brexit Britain do not offer freedom of movement for people, capital and goods.