Senior Cabinet minister Michael Gove is self-isolating after a family member, who he had been in contact with, began experiencing symptoms of coronavirus.
The Chancellor of the Duchy of Lancaster, part of the government's lead team giving advice on Covid-19, remains "well" but must stay in isolation, as per public health instruction.
With Prime Minister Boris Johnson in intensive care after his coronavirus symptoms worsened, it had been expected Mr Gove would continue to play a leading role in the government's response to the outbreak.
He will continue to work from quarantine and in morning interviews before his isolation was revealed, he said the "work of government goes on".
Mr Gove said Mr Johnson is receiving the "very, very best care" and insisted that the government machine is continuing to function.
"We're all working together to implement the plan the Prime Minister set out in order to try to ensure that we can marshal all the resources of government, indeed all the resources of our country, in the fight against this invisible enemy," he told BBC Breakfast.
"The work of government goes on.
"We have a superb Civil Service and they have ensured that the machinery is there for decisions to be made by ministers, by medical and scientific experts, and for those decisions to be followed through in a way which enables us to help those at the front line."
With Mr Johnson in intensive care, Foreign Secretary Dominic Raab, who is "deputising", is leading the Government's daily coronavirus "war cabinet" meetings.
Mr Gove, who has known Mr Johnson since they met as students, said the Prime Minister being in intensive care is "terrible".
He told Good Morning Britain: "We are just hoping and praying that he pulls through. It was a shock yesterday to hear the news about his going into intensive care."
He added: "We're desperately hoping that Boris can make the speediest possible recovery."