Sir Simon Stevens warned the health service has never been in a more precarious position.
But he also shed some positive light on the speed of the vaccination programme, saying 140 jabs are being delivered “every minute”.
Speaking to the BBC’s Andrew Marr Show, he said: “The facts are very clear and I’m not going to sugar-coat them, hospitals are under extreme pressure and staff are under extreme pressure.
“Since Christmas Day we’ve seen another 15,000 increase in the inpatients in hospitals across England, that’s the equivalent of filling 30 hospitals full of coronavirus patients.
“Staggeringly, every thirty seconds across England another patient is being admitted to hospital with coronavirus.”
Sir Simon warned that the NHS is facing the most “unique” situation in its 72-year history.
He said: “It’s become glib to talk about this as the worst pandemic in a century, but that is clearly correct.
“We have got three-quarters more Covid inpatients now then we had in the April peak.
“Although we are seeing some promising signs of the steadying of the infection rates, the fact is they are still far too high and, among some age groups, still rising.”
But he also spoke positively about the vaccination programme, saying the NHS in England is jabbing “four times faster” than people are newly catching the virus.
He said: “We will start testing 24/7 in some hospitals over the course of the next 10 days.
“But we are at the moment vaccinating at about 140 jabs a minute and yesterday (Saturday), a quarter of a million people got their vaccinations on the NHS.
“I’m pretty confident by the time we get to the end of today, Sunday night, we will have perhaps done 1.5 million vaccinations this past week, that’s up from around a million the week before.”
It comes as more than 3.5 million people in the UK have now received their first dose of a vaccine, with some 324,000 doses administered in the space of 24 hours.
Sir Simon also predicted that lockdown could be eased “gradually” around spring and summer time.
However, he said this would depend on the effect of new variants of coronavirus.