"The prime minister is the head of this government and the prime minister runs this government. The prime minister has always been in charge," junior health minister Edward Argar told Sky News when asked who had been in charge until now.
Asked about Britain's COVID-19 tracing system, he said: "We are into the thousands being successfully traced at the moment, I don't have the precise figures because we are working with the UK Statistics Authority to agree the process to make sure that they accept it's reliable."
Johnson will chair a new committee on strategy, while another on operations will be led by senior minister Michael Gove, the Telegraph reported.
Opposition Labour leader Keir Starmer said there was growing concern the government was now "winging it".
"I am putting the prime minister on notice that he has got to get a grip and restore public confidence in the government’s handling of the epidemic," he said in an interview with the Guardian.
"If we see a sharp rise in the R rate, the infection rate ... responsibility for that falls squarely at the door of No 10. We all know the public have made huge sacrifices. This mismanagement of the last few weeks is the responsibility of the government."