Sir Patrick Vallance said that would be expected to lead to about "200-plus deaths per day" a month after that.
It comes as the PM prepares to chair a Cobra emergency committee meeting on Tuesday morning, then make a statement in the House of Commons.
On Monday, a further 4,368 daily cases were reported in the UK, up from 3,899.
A further 11 people have also died within 28 days of a positive test, although these figures tend to be lower over the weekend and on Mondays due to reporting delays.
Speaking at Downing Street alongside chief medical adviser, Prof Chris Whitty, Sir Patrick stressed the figures given were not a prediction, but added: "At the moment we think the epidemic is doubling roughly every seven days.