Junior doctors Dr Rachel Clarke and Dr Dagan Lonsdale will stay outside the DH for 12 hours a day, seven days a week in a bid to force the health secretary to reopen talks.
The pair pointed to Mr Hunt's claim that his 'door is open' to junior doctors, and called on him to let them in to discuss how to resolve the junior doctor contract dispute.
The protest comes as junior doctors prepare for an unprecendented full walkout later this month on 26 and 27 April.
Junior doctor strikes
Protester Dr Lonsdale said: 'I am here because I have a duty to raise concerns about the safety of patients within the NHS. It is unbelievable that David Cameron and Jeremy Hunt have chosen to ignore 54,000 whistle-blowers. I am here to remind them of their responsibilities as guardians of the NHS and to implore them to return to talks.'
Dr Clarke said: 'None of us can understand why Jeremy Hunt is burying his head in the sand and refusing to talk when an all-out strike is days away. Grassroots doctors are absolutely desperate. Dialogue is so obviously the only way to end this dispute.'
GP registrar Dr Marie McVeigh told GPonline that she and other members of the Just Health campaign - which has crowdfunded more than £100,000 to support legal action against the government over the contract imposition - were supporting the latest protest.
Members of the campaign had taken annual leave and come out between shifts to support the two protesters outside the DH, she said.
'We've had loads of MPs coming out to speak to us,' she said. 'We've just had [Labour shadow health secretary] Heidi Alexander - she was supportive of the action, and agreed that talking is the only way to manage the situation and avert the strike.'
Dr McVeigh spoke to GPonline earlier this month from a picket line outside a London hospital, warning that details of the junior doctor contract published by the government were worse than expected.