Fourteen patients were treated in a corridor within the A&E department on Sunday, a hospital spokesman said.
The daughter of one elderly patient, who did not wish to be named, said it was "horrendous" and her mother waited 18 hours for a bed.
The trust, rated inadequate last year, said there had been a 20% rise in ambulance arrivals over the past year.
Up to 98 ambulances went to Worcester and 56 to the Alexandra Hospital on Sunday.
More updates on this story and other in Hereford and Worcester.
Worcestershire Acute Hospitals NHS Trust said it had to amend capacity in Worcester and at its other hospital in Redditch, opening an extra 20 beds.
The corridor is able to take patients and is staffed when needed, it said.
"Sunday in particular, we believe, was our busiest day ever," a spokesman said. "We did work with the ambulance service to look after patients for a short period. This is something we have done with the ambulance service before.
"We have and are continuing to put in additional staffing to support this increase in demand as well as increasing the size of our A&E."
The trust said it accepted that some ambulance journeys could have been managed differently, and said its main response of admitting more patients was "not working for our hospitals or for our patients". A new emergency department is expected to be open later this year.
The 84-year-old patient's daughter told BBC News her mother was sent home with antibiotics because there were no beds available but despite being readmitted a day later she still waited several hours for a bed.
She said there were two "banks" of mostly elderly patients were on either side of the corridor.
West Midlands Ambulance Service said it saw a 20% increase in 999 calls in Worcestershire on Sunday, and said journeys to Worcester had "steadily increased" since a recent reconfiguration of services from Redditch.
Worcestershire Royal Hospital has experienced what doctors believe was its busiest day ever at the weekend.