Rose Polge was last seen on Friday and her car has since been discovered by police near cliffs at Anstey’s Cove, near Devon.
A note was found in her car that contained a number of personal messages addressed to family members and made a passing reference to Hunt.
A search operation involving the police and the RNLI has, so far, yielded no trace of her.
The Daily Mirror and Metro newspapers both carried the story on their front pages today with references to Hunt, while the BBC also featured the story but did not include the Health Secretary’s name in the headline.
The stories pile additional pressure on Hunt, who has been widely criticised for his handling of the junior doctors' strike. Hunt has pledged to impose an unpopular contract on junior doctors after talks with the British Medical Association failed to yield an agreement, leading to strikes called by the doctors' union.
A Department of Health spokeswoman told PRWeek this morning that the issue was a police matter and it would make no comment other than: "Our thoughts are with Dr Polge's family and friends at an extremely difficult time."