Boris Johnson has admitted the public are “furious” at the continued coronavirus restrictions but said scientific advice suggested a vaccine or mass testing would be possible by spring.

The prime minister said people should “behave fearlessly but with common sense” and carry on with their lives as much as possible while obeying the rules.

He also defended his own demeanour, which has led to questions about his health and whether he has the will to continue to impose restrictions, saying it would be “inappropriate” for him to behave “with buoyancy and elan”. He said it was “drivel” and “balderdash” to say that he was still feeling significant after-effects of the virus.

Johnson told BBC One’s The Andrew Marr Show: “I think the reality is this is a government that is facing an unprecedented crisis and I think if people wanted me to approach it with the sort of buoyancy and elan and the qualities I usually bring to things, I think people would think that was totally inappropriate.

“The struggle we have now is to contain that pandemic and yet to keep our economy moving … And what I can certainly tell you is that as soon as we have done what is necessary and we have got the virus under control … then you will see this country and this government and this country really accelerating our progress.”

Speaking during the Conservatives’ virtual conference, Johnson said he hoped a radical new direction would be possible within six months.

“What I hope, and I believe very strongly, is that in the course of the next weeks and months, the scientific equation will change and we will start to see progress, whether it is on vaccines or on testing, that will enable us to take a different approach,” he said. “But for the moment, that is the balance that people have to adopt, that is the line we have to follow.”

He warned that the pandemic was “going to continue to be bumpy through to Christmas, it may even be bumpy beyond” and said he appreciated the fatigue that people were experiencing.

Johnson added: “They’re furious at me and they’re furious for the government, but… this is the only way to do it … As prime minister I couldn’t take a course that could expose us to tens of thousands more deaths in very short order.”

Asked whether he had “overpromised and underdelivered” during the pandemic, he said: “Actually, if you look at what happened during the course of the pandemic, we did turn the tide in the sense that the numbers went massively down. I think most people would say that the lockdown had turned the tide. We now have, as I constantly warned, a second spike.”

He said the 10pm curfew would only work if people were consistent, but would not elaborate on the scientific advice behind the measure, saying only that “by curtailing the hours you can reduce the transmission”.

“Obviously it makes no sense if, having followed the guidance for all the time in the pub they then pour out into the street and hobnob in such a way as to spread the virus.”

The prime minister acknowledged frustrations with the NHS test-and-trace system, which is falling far short of his goal for in-person test results to be returned within 24 hours.

“I’m not going to claim that the service is perfect, because it isn’t,” he said, but added that it had “made a huge difference to our ability to see where the virus is and where it is spreading, in which groups it is most prevalent, and it is helping us a huge amount”.

Having suffered Covid-19 himself, and with Donald Trump in hospital with the virus, Johnson emphasised the importance of tackling obesity. He said: “Obesity … is one of the problems that this country needs to address. Not just because it threatens all our health but in the long term we need to tackle it to reduce the pressures on the NHS.”

He added: “The issue is when I got this wretched thing I was, alas, too fat. If I may say so, this is a teachable moment for our great country because we are one of the greatest places on Earth but, alas, as a nation we are slightly too fat. We are fatter than virtually anybody else in Europe, apart from the Maltese for some reason, and we need to think about this. I don’t wish to cast any aspersions on my Maltese friends.”