The warning comes as Mr Javid was appointed within hours of Matt Hancock's resignation on 26 June after the Sun newspaper revealed he had kissed an aide at the DHSC, in a breach of COVID-19 rules.
In his resignation letter to prime minister Boris Johnson, Mr Hancock wrote: 'We have worked so hard as a country to fight the pandemic. The last thing I would want is for my private life to distract attention from the single-minded focus that is leading us out of this crisis.
'I want to reiterate my apology for breaking the guidance, and apologise to my family and loved ones for putting them through this.'
Mr Hancock added: 'We owe it to people who have sacrificed so much in this pandemic to be honest when we have let them down as I have done by breaching the guidance.'
I have resigned as Health Secretary pic.twitter.com/eyWi1AA19i— Matt Hancock (@MattHancock) June 26, 2021
BMA chair Dr Chaand Nagpaul said: 'Sajid Javid has a huge and urgent task ahead. He must ensure completing the rollout of the adult vaccination programme at rapid pace to control spiralling infection rates.
'He must also put forward a credible plan to tackle a backlog of care of unprecedented scale while at the same time rebuilding the trust of doctors and the wider healthcare workforce.'
The new health and social care secretary takes on the role at a critical time in the COVID-19 pandemic, with 84% of the UK adult population having received a first dose of vaccine and nearly two thirds both doses, but with cases continuing to rise.
More than 100,000 positive COVID-19 tests have been recorded in the past week alone UK-wide, with the average daily figure of 14,864 over the past week the highest recorded since early February. The government has also said that figures for Sunday 27 June in England were lower than they should have been because of a 'technical issue'.
Dr Nagpaul warned: 'Frontline doctors and other staff have gone above and beyond time and time again over the course of the last 18 months, with many suffering from burnout and mental ill health as a result.
'The new secretary of state must show he understands this challenge and must also be willing to listen to the voice of the frontline on the government's plans for sweeping changes in the running of the NHS in the upcoming Health and Care Bill.
'It is imperative that doctors are able to take leave, rest and regroup before tackling the biggest waiting list the NHS has ever seen. And we would urge Mr Javid to think again about the government’s 1% pay proposal which, on top of punitive pension changes, risks driving a generation of senior, experienced doctors into early retirement.
'Sajid Javid must now show that the government understands the value of frontline healthcare workers and their critical role in the future of our NHS. We look forward to meeting Mr Javid as soon as possible.'
Mr Javid said: 'I’m incredibly honoured to take up the post of health and social care secretary, particularly during such an important moment in our recovery from COVID-19. This position comes with a huge responsibility and I will do everything I can to deliver for the people of this great country.
'Thanks to the fantastic efforts of our NHS and social care staff who work tirelessly every day, and our phenomenal vaccination programme, we have made enormous progress in the battle against this dreadful disease. I want our country to get out of this pandemic and that will be my most immediate priority.'
Outgoing health and social care secretary Mr Hancock completed almost three years in the role after being appointed by former prime minister Theresa May in July 2018. His departure leaves him just short of joining the UK's top 10 longest-serving health secretaries.