The National Police Chiefs' Council (NPCC) figures obtained as part of a Freedom of Information request by BBC show an average of 35 referrals a month in the year to July 2016 -- up from 21 a month the previous year.
The NPCC said that following the assessment in England and Wales, one in 10 were found to be vulnerable to radicalisation and offered support.
Since July 2015, public bodies in the UK have a legal duty to report people considered at risk of being drawn into terrorism.
There was no breakdown of how many of the 420 referrals in the 12 months to July 2016 were for patients and how many for staff.
A UK Department of Health spokesperson said, "Radicalising vulnerable people and encouraging terrorist acts is something which NHS staff should treat as a safeguarding issue."
The UK government claims the referrals are part of its Prevent programme that safeguards people at risk of getting radicalised.
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