Around 55,000 people in the UK have coronavirus, the Government's chief scientific adviser has said, as the NHS moved to cancel all non-emergency surgery and 71 people are now known to have died.
Sir Patrick Vallance told MPs the hope was to keep the death toll to under 20,000 as he told of the huge amount of strain the health service will be under from Covid-19.
It comes as Prime Minister Boris Johnson told his Cabinet the coronavirus pandemic is a "war" that must be won as he set out plans for a team to tackle the outbreak and economic chaos.
NHS England chief executive, Sir Simon Stevens, also told MPs the NHS would be "flat out" helping coronavirus patients for the next four to six months.
He has sent a letter to hospitals telling them to prepare for a big influx of patients requiring ventilation and ordered moves to cancel non-emergency surgery by April 15 at the latest, alongside the discharge of medically fit people to free up beds.
During a hearing of the Health Select Committee, chairman Jeremy Hunt asked Sir Patrick whether the expected death rate was one fatality for every 1,000 cases, which would mean that there are "potentially 55,000 cases" at present.
Sir Patrick said: "We've tried to get a handle on that in Sage (Scientific Advisory Group for Emergencies) and if you put all the modelling information together, that's a reasonable ballpark way of looking at it.
"It's not more accurate than that."
He said the stringent measures introduced on Monday should "have a very significant effect on the peak" and lead to a reduction in cases and deaths after two to three weeks.
Asked whether it was hoped that deaths could potentially get below 20,000, Sir Patrick said: "That is the hope that we can get it down to that. To put that into perspective, every year in seasonal flu the number of deaths is thought to be 8,000.
"If we can get numbers down to 20,000 and below, that's a good outcome in terms of where we would hope to get to with this outbreak.
"But that's still horrible, it's still an enormous number of deaths and an enormous pressure on the health service, and having spent 20 years as an NHS consultant as well as an academic, I know what that looks and feels like."
He warned that much was still unknown about what would happen once people are released from isolation and no longer told to undertake social distancing.
Sir Patrick said "that's one of the big unknowns in this which we are going to have to think about very carefully".
But he refused to be drawn on suggestions that the Government's measures could have to be kept in place for 18 months to prevent the virus resurging.