Leaders at the Queen Alexandra Hospital in Portsmouth have said demand is 'outstripping capacity' and elective care will be 'inevitably compromised'.
The Medical Director said pressures in the city were "unheard of" with bed occupancy rates above 99%, despite falling numbers of Covid patients.
Dr John Knighton said the hospital is prioritising cancer care no matter what and it will be doing everything it can to minimise the effect on elective, planned work.
However he said there may come a point at which it is "inevitably compromised."
In a report, the trust said 330 people were visiting the hospital's emergency department each day. Just under half of these were being brought in by ambulance.
Responding to questions about how the trust planned to manage an expected rise in demand on its services over the coming months, he said it was focusing on 'marginal gains on a number of different fronts'.
He said: "Some of that is going to mean managing the demand at our front door differently.
"We are going to have to make sure that all of our internal processes are as slick, as good and as effective as they can be to waste as little time as possible."