East Midlands Ambulance Service (Emas) took 3,000 calls on Sunday - a third more than usual - with most coming in the early hours.
It said it was sustained pressure into the late afternoon that led to an incident being declared.
Managers also had to ask neighbouring services for help.
Emas, which covers Derbyshire, Leicestershire, Rutland, Nottinghamshire, Lincolnshire and Northamptonshire, said the incident was declared at 17:30 GMT on Sunday and scaled back at 21:00 GMT.
It led to paramedics having to reduce their meal breaks from 45 to 20 minutes to keep more ambulances available.
Chief operating officer Dave Whiting said it was a "critical event".
He said: "We faced the busiest 48 hours we've ever faced in the ambulance service.
"Yesterday, where we would normally expect to take 2,000 emergency calls, we took 3,000. A large proportion of those were in the first six hours which we would expect to see during New Year's Eve night."
He added: "Rather than see a drop off in activity during the day on New Year's Day which we typically see, the demand kept coming right through to the evening."
The expected spike in the early hours of Sunday saw a large number of alcohol-related incidents, but during the day it was a "broad range" of calls.
Mr Whiting said a investigation and debrief would try to establish why there was such high demand on Sunday afternoon.
Emas - which is already the worst performing ambulance service in England - said that throughout December, 57% of all calls were categorised as the most serious compared with the expected rate of 42%.
Figures over the whole festive period were also higher than previous years.
An ambulance service declared its first "critical event" during its busiest ever 48 hours, taking 1,000 more calls on New Year's Day than normal.