Downing Street needs to accelerate planning for exiting the coronavirus lockdown because contact tracing, testing and social distancing will be needed “indefinitely” until a vaccine is discovered, Prof Neil Ferguson, one of the leading epidemiologists advising the government, has said.

Ferguson, whose team at Imperial College provided the modelling that led to the lockdown, said data suggested infections were coming down but life would not get back to normal quickly after the lockdown is eased.

As ministers prepare to extend the lockdown for three weeks, attention is turning to what happens when it might be possible to ease the restrictions.

Matt Hancock, the health secretary, expressed extreme frustration about being asked to explain the government’s exit strategy in broadcast interviews on Wednesday, saying: “Everybody wants to know what the future looks like. The question is how do we best get through the crisis and how do we get the numbers down.”

He added: “The thing is this: how we communicate as government, as ministers, has a direct impact on the cases we have and the people who die. Because clarity of messaging that people need to stay at home ... that saves lives. This core messaging has a direct impact on how many people follow the guidelines. The scientists can say what they like, the commentators can say what they like, but we will do our best by dealing with this virus.”

Hancock said Ferguson “advises government, he is not in the government”.

Ferguson said he would like to see the government move faster to put a plan in place for what happens when measures are partially lifted, saying he did not see the same level of planning going on that was put into Brexit.

Ferguson told BBC Radio 4’s Today programme: “There’s a lot of discussion. I would like to see action accelerated. I don’t have a deep insight about what’s going on in government, but decisions need to be accelerated. We need to put in place an infrastructure, a command and control structure, a novel organisation.

“I’m reminded we had a department for Brexit for government. That was a major national emergency and we are faced with something even larger than Brexit. And yet I don’t quite see the evidence for that level of organisation. I’d like to see measures accelerated.”

The Guardian reported on Wednesday that there was no central plan for exiting the lockdown yet, even though ministers have been floating ideas about which parts of the population might have restrictions lifted first – from younger people to the immune or different sectors of the economy.

Ferguson said it was necessary to ease restrictions at the right time but added: “We will have to retain some level of social distancing indefinitely until we have a vaccine available.”

He said there now needed to be a “single-minded emphasis on scaling up testing and contact tracing”.

He argued that a huge infrastructure of testing and contact tracing would need to be in place in order for the lockdown to be lifted without further peaks, pointing to the model of South Korea, which has been suppressing new outbreaks.

“Without that, our estimates show we have relatively little leeway. If we relax measures too much then we will see a resurgence in transmission,” he said.

Ferguson’s remarks suggest he believes the UK should return to a strategy of containment, which was abandoned by No 10 and its chief scientific and medical advisers early in the epidemic, to the concern of public health experts.

Jeremy Hunt, the former health secretary, is one of those who has been arguing for weeks that mass community testing and tracing is necessary, while the government was at that point insisting that a test for antibodies to prove immunity was the most important strategy. Since then, antibody tests have proved hard to develop with any accuracy.

Ministers have been trying to ramp up testing since early March, with a target of 25,000 daily by mid-April and 100,000 daily by the end of the month. Hancock denied the existence of the 25,000 target on Wednesday but on Thursday he claimed the government had now reached capacity to do 25,000 tests a day with the help of new drive-through centres for NHS workers.