Stephen Powis, the medical director of National Health Service England, warned the public against complacency and said everyone had to play their part in hindering the spread of the virus.
The number of confirmed cases stood at 17,089 on Saturday morning. The death toll rose by 260 in a day to 1,019, the seventh highest toll in the world behind Italy, Spain, China, Iran, France and the United States.
When asked if Britain was on the same trajectory as Italy, where the death toll has passed 9,000, Powis said that if the public adhered to the nationwide lockdown the total toll could be kept below 20,000.
“If it is less than 20,000... that would be a good result though every death is a tragedy, but we should not be complacent about that,” he said at a news conference in Downing Street.
Prime Minister Boris Johnson became the first leader of a major power to announce a positive test result for coronavirus on Friday. He is self-isolating in Downing Street but still leading the UK response to the crisis.
Britain is bracing for the epidemic to peak in the coming weeks, and is building field hospitals in London, Birmingham, Manchester and Cardiff to bolster its state-run National Health Service (NHS).
The government, which had been criticized by some doctors and nurses for not providing them with enough protective gear and testing kits, said on Friday it was introducing a much bigger testing regime, with checks for health workers in England.
Frontline medical staff in Wales, Scotland and Northern Ireland are already being tested.