Current pressure on the NHS is “sustainable”, according to a health minister, who denied the government had a “plan C” that would ban the mixing of households at Christmas in England if cases continued to rise.

Edward Argar told BBC Radio 4’s Today programme that while the NHS was “under huge pressure” it was not the right time to introduce any additional measures to control the spread of Covid.

The British Medical Council chair, Dr Chaand Nagpaul, accused ministers of being “wilfully negligent” after the health secretary ruled out immediately implementing the government’s coronavirus “plan B”.

Nagpaul said: “It is wilfully negligent of the Westminster government not to be taking any further action to reduce the spread of infection, such as mandatory mask wearing, physical distancing and ventilation requirements in high-risk settings, particularly indoor crowded spaces. These are measures that are the norm in many other nations.”

Argar urged people to get vaccinated to help “ease that pressure on the NHS”. He said plan A was still working, adding: “It’s a race … between the vaccines, and getting those in people’s arms, and the virus. We’re still winning that race at the moment, but it’s narrowing, that lead is narrowing. So what we need to do is that sprint for the line.”

On Wednesday the health secretary, Sajid Javid, predicted new infections could hit a record 100,000 a day and urged millions of eligible people to come forward for booster jabs. Javid urged people to wear masks in crowded places and test themselves before going to Christmas parties.

But the government has been accused of sending 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.

On Thursday a leading virologist said the UK was probably already close to 100,000 cases a day. Dr Chris Smith, from the University of Cambridge, said half of Covid cases were asymptomatic, meaning the number of active cases in the UK was likely far higher than currently recorded, “we just don’t know about lots of them”.

Pushed about Conservative MPs wearing masks, Argar said there was a “leadership role for members of parliament on all sides”, adding: “I think it’s for those individual members of parliament to read the guidance, consider it, bear in mind what Sajid has said and reach their own views.”

Argar was asked about comments from the UK government’s chief scientific adviser, Sir Patrick Vallance, who said it was important to act before it appeared necessary.

Argar told Sky News: “I think what Patrick’s saying there is you’ve got to look ahead. We know that you have a lead time of two weeks roughly between infections and hospitalisations, and for the two weeks between, sadly, hospitalisations and deaths in the most serious cases.

“I think what Patrick saying is always look to the future, consider when is the right moment to act … I don’t think we’re at that point yet.”

Argar denied there was a plan C being considered by the government which would ban the mixing of households at Christmas, as reported in the Daily Telegraph. “That isn’t something that is being actively considered,” he said.

Asked on Sky News how bad the situation in the NHS would have to get before the government moved to plan B, he said it would not “be appropriate to set an arbitrary figure, X number of infections, X number of hospitalisations”.

Bed occupancy levels were one measure of whether the pressures on the NHS were sustainable, he told Times Radio. With 95,000 beds across the hospital system available, 7,000 were occupied with Covid patients and 6,000 were unoccupied.

“We do have a degree of headroom at this time, we continue to monitor it hour by hour, day by day, to see what’s happening with those figures, both in terms of infection, but also crucially in terms of hospitalisation,” he said. “Our assessment at the moment is the most effective way to continue to control that is for people to get those booster jabs.”

He said people should no longer wait to be invited to get their booster vaccine if the right amount of time had passed, as they could book it themselves online.