Blasting the current strategy, he told the newspaper: 'What we should have done is crush the epidemic and then keep it down.'
Professor Costello is set to give evidence to the Commons Health Committee today, where he is expected to warn of repeated waves in Britain.
In the same session, Mr Hancock will face questions from MPs over the response to the coronavirus crisis in Britain.
Yesterday Number 10 announced Britain's lockdown would be extended for at least another three weeks despite growing alarm at the economic consequences.
Professor Costello accused the Government of being a 'one-club golfer' for relying solely on a lockdown working.
He said: 'It should be combined with testing, tracing and digital apps that have been used so successfully in South Korea.'
South Korea bucked the global trend and decided against a lockdown to contain its COVID-19 outbreak - which peaked in February.
Officials at the Korea Centers for Disease Control and Prevention have only recorded 10,000 cases of the deadly virus. They tested thousands more suspected cases.
Britain has promised to carry out 100,000 tests a day by the end of April - but figures show it is currently carrying out fewer than 20,000 swabs daily.
Data last night showed only 18,665 tests were performed on Wednesday, despite the claim from the PM's spokesman that the UK can conduct 35,000 a day.
The UK gave up on testing all suspected patients early on in the outbreak, to the fury of the WHO which said the pandemic cannot be fought 'blindfolded'.
And ministers also gave up on tracing infected patients' close contacts, allowing the virus to spread effectively unchecked.
Research for MailOnline by Redfield & Wilton found 80 per cent would not feel safe going back to everyday life at the moment
Around half the public are now resigned to the draconian 'social distancing' curbs being in place into June
A graph showing the number of new infections in various countries, starting on the day they first recorded five infections. The graph shows a rolling average, meaning it shows trends in the data rather than exact figures. The Y-axis is scaled due to the large difference in numbers between worst-hit countries such as USA and Britain, and countries which were less badly hit, such as Australia and South Korea. In an evenly-scaled graph, the worst-hit countries' readings would show a much steeper curve
Professor Costello also said the Scientific Advisory Group for Emergencies (Sage) - Number 10's main advisory panel - 'have got most of it wrong'.
It comes as the Government is under growing pressure to reveal the identities of the dozens of experts who sit on the group.
MPs have warned that the lack of transparency could harm public confidence in the official response to the crisis, which has already attracted criticism.
Government sources said members of the group and its committees had received death threats, fuelled by Britain's response to the pandemic.
It comes as Dutch researchers yesterday found that only three per cent of the population has developed antibodies to the SARS-CoV-2 virus.
The number is an indication of what percentage of the Dutch population may have already had the disease.
Ministers in the European country - home to 17million people - said it means several hundred thousand people may have already been infected.
One study of the town at the centre of Germany's outbreak found as many as 15 per cent of people may have already been infected with the virus.
Other research has showed that many recovered coronavirus patients have barely-detectable signs of past infection.
A Chinese study last week revealed a third of past patients have very low levels of antibodies in their blood, which could make them hard to test for.
British experts said the finding explains why the UK has repeatedly delayed rolling the tests out to the public, despite promises they were in the pipeline.
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