Prof Horby, chairman of the New and Emerging Respiratory Virus Threats Advisory Group (Nervtag), said there may be "early signs that something is beginning to bite" due to the restrictions - but if they did not then stricter measures would be needed.
He told the BBC's Andrew Marr Show: "I really hope people take this very seriously. It was bad in March, it's much worse now.
"We've seen record numbers across the board, record numbers of cases, record numbers of hospitalisations, record numbers of deaths."
media captionProfessor Peter Horby explains why the new Covid-19 variant is up to 70% more transmissible
Prof Horby said tougher measures might include those during the March lockdown, such as people only being able to exercise once a day and stricter rules about meeting people.
"We are in a situation where everything that was risky in the past is now more risky," he said.
Prof Horby said early signs were encouraging that the vaccines would be effective against the new Covid variants - first identified in the UK and in South Africa - and he did not want people to "hide under the duvet".
"We can see the end game now," he said.