Politicians have a responsibility to set an example in the battle against Covid, including wearing masks in crowded spaces, Sajid Javid has suggested as he predicted new infections could hit a record 100,000 a day.

With the government under mounting pressure to impose measures to control the virus, Javid warned “this pandemic is not over” and insisted he would do “what it takes” to protect the health service. But he said: “We don’t believe that the pressures currently faced by the NHS are unsustainable.”

Javid urged millions of eligible people to come forward for booster jabs, saying this was key for people being able to “keep their freedoms”, but declined to say how high infection or hospitalisation rates would need to reach before measures are reimposed.

He was pressed on the risks of mixed messages, with most Conservative MPs declining to wear masks in the House of Commons or in packed cabinet meetings, and the business secretary, Kwasi Kwarteng, encouraging the public to book Christmas parties.

Javid conceded that this was an issue. “I think that is a very fair point. As I say, we’ve all got our role to play in this,” he told a Downing Street press conference alongside Jenny Harries, head of the new UK Health Security Agency, and Stephen Powis, medical director of NHS England.

Javid said: “We, the people standing on this stage, we play … our public roles as secretary state, as someone from the NHS, as the head of UKHSA. But we also have a role to play in setting an example as private individuals as well, and I think that’s a very fair point, and I’m sure a lot of people will have heard you.”

Previously, ministers have brushed aside concerns about mask-less Tory MPs crammed into the Commons chamber, a compact arena with limited ventilation, saying it is within guidelines as the MPs are colleagues.

Javid struck an overall sombre tone at the conference, repeatedly stressing the virus has not gone away despite the absence of any formal restrictions on daily life in England.

On Wednesday more than 49,000 new Covid cases were reported in the UK, alongside 179 deaths, and Javid repeated a warning made this summer that daily infection rates “could yet go as high as 100,000”.

“We must all remember that this virus will be with us for the long term, and that it remains a threat,” he said. “A threat to our loved ones and a threat to the progress that we’ve made in getting our nation closer to normal life.”

The British Medical Association said on Wednesday it was “categorically” now time to activate plan B, which would see a return to coronavirus measures in England.

Britain’s largest doctors’ union added that it was “incredibly concerning” and “wilfully negligent” of the government to refuse to take further action to tackle the crisis.

Dr Chaand Nagpaul, BMA council chair, accused ministers of taking their “foot off the brake” by giving millions of Britons the false impression that “the pandemic is behind us”.

“Only last week two select committees found the UK was an international outlier when it came to public health policy during this crisis,” he added. “We are rapidly approaching a position where, yet again, the government is delaying for too long, and equivocating over taking action.

“This is the time to learn the lessons of the past and act fast, or else we will face far more extreme measures later.”

On Tuesday, the NHS Confederation said the government must immediately press ahead with its “plan B” for containing the virus or risk derailing efforts to tackle the backlog of 5 million patients.

Matthew Taylor, its chief executive, said Javid’s warnings of up to 100,000 cases a day emphasised the need for action. “The message from health leaders is clear – it is better to act now, rather than regret it later.”

Javid said he had great respect for the NHS Confederation, which represents healthcare providers, but said he would not be moving to plan B “at this time”.

He underlined the fact that ministers would be “staying vigilant, preparing for all eventualities” however, and said that fresh restrictions might need to be imposed if people do not behave cautiously.

If Javid’s warning of 100,000 cases a day came to pass, that would be higher than at any stage during the pandemic. The highest recorded daily figure for reported cases was 68,053 on 8 January.

The health secretary previously suggested cases could hit 100,000 in the summer, when infections rose sharply as restrictions were lifted – but they went on to peak above 60,000 in July before falling away.

He said the government would be redoubling its efforts to administer booster jabs to the over-50s and the clinically vulnerable. The NHS has already administered 4m top-up doses but Javid urged others to come forward.

“We’ve got the jabs: we just need the arms to put them in,” he said, calling it a “national mission” to roll out the vaccine. He urged people to come forward for their booster vaccine dose, “not just to save lives, but to keep your freedoms too”.

Asked about problems with the current rollout of vaccinations, with charities representing immunocompromised people saying only about 40% have so far received news of their third jab, Javid also accepted there had been issues.