Imperial College Healthcare, an NHS Trust with five hospitals across north-west London, prioritises patients who have been assigned an interpreter.
The trust's aim is to avoid additional charges from the interpreting service.
It is unclear whether NHS trusts nationwide take this approach, but last night it sparked a row, with Tory leadership hopeful Robert Jenrick claiming the approach lets down British NHS patients.
The former immigration minister told The Mail on Sunday: 'Brits are already waiting too long for treatment. The last thing they should be subjected to is the indignity of being pushed to the back of the queue.
'This is yet more evidence of the pressure mass migration places on our public services and the difficulties integrating such unprecedented numbers.
'Non-English speakers shouldn't be given a queue pass.