Nearly nine in 10 general and acute beds at the Royal Devon University Healthcare Trust were occupied in the last week of December, as flu cases increased, new figures show.
NHS leaders have warned pressure on hospitals is "nowhere near letting up" this winter.
The most recent NHS situation report for this winter shows Royal Devon University Healthcare NHS Foundation Trust had an average of 991 out of 1,128 beds occupied (88%) in the week to December 29.
Across England, 89% of available beds were occupied in the most recent week – an improvement on 93% the previous week.
Despite this, the average number of flu patients in beds each day last week reached 4,469, up 17% from the previous week. Of these patients, 211 were in critical care.
At the Royal Devon University Healthcare Trust, an average of 61 patients had flu in the week to December 29, with four in critical care.
It was a rise from 35 patients the week before.
Professor Julian Redhead, NHS national clinical director for urgent and emergency care, said the figures "show the pressure from flu was nowhere near letting up before we headed into the New Year" and cases are "rising at a very concerning rate."
The data also showed an average of 528 hospital beds in England were filled each day by patients with diarrhoea and vomiting or norovirus-like symptoms.
Meanwhile, the average number of beds occupied by patients with Covid-19 stood at 1,184.
In the Royal Devon University Healthcare Trust, 10 patients had diarrhoea and vomiting or norovirus-like symptoms, and eight patients tested positive for Covid-19.
Prof Redhead said: "On top of flu there is also continual pressure from Covid, while RSV and norovirus hospital cases are also higher than last year, with hospitals putting in place an extra 1,300 beds last week than the same time last year in expectation of this continued pressure from viruses and other demand."
He added those who are vulnerable or have respiratory conditions should keep warm and make sure their regular medication is stocked during the cold weather.
NHS Confederation chief executive Matthew Taylor said: "The NHS has done all it can in advance to mitigate risks to patients this winter, but we should be under no illusions that the service is in a position of national vulnerability as the intense pressures we are now seeing start to grip local services."
He added the statistics reveal the NHS is facing "huge demand, from sicker patients, with very high levels of flu".
"The next two to three weeks will likely be the busiest period of the year for many local services and we need to acknowledge the strain that this will place on staff and services," he said.