Patients in Sussex have complained of missing hospital appointments and of having to book taxis after a private firm took over transport services.
The problems emerged on 1 April as Coperforma began its first day of operations across the county.
Kidney dialysis patient Roger Boniface said he was picked up nearly five hours late for his appointment on Monday at the Royal Sussex County Hospital.
Coperforma said there had been problems with data transfer and booking details.
Mr Boniface uses patient transport services three times a week to take him from his home in Shoreham to the hospital in Brighton.
He said: "Eventually an ambulance arrived [at 11:40 BST] then I had my dialysis for four hours, and I was ready to go home at [19:15].
"Then I was told by the hospital that the patient transport people had all gone home, and they would get me a taxi."
Other patients complained of ambulances not turning up at all, while hospitals said they had to pay for taxis as well as overtime for staff dealing with the problems caused.
In a statement, Coperforma apologised "unreservedly" to patients and staff affected, and said its non-emergency patient transport service had been "unacceptable".
However, it added that some of the patient data had been "unnecessarily withheld" by the Patient Transport Bureau, the body that formerly managed journeys, until 23:15 BST on 31 March.
"The late timing of the data... together with issues about the quality of that data presented huge challenges to its transfer into the booking system.
"These factors resulted in many more thousands of calls to the booking line than expected, diverting staff from delivering the service expected by patients and NHS staff," it said.
The Sussex Clinical Commissioning Groups, which commissions patient transport services, admitted the problems had been due to "a number of complex issues, including problems with data transfer and patient booking information".
Apologising to all users of the service, it said it was working with Coperforma "to ensure the service meets the needs of our population as quickly as possible".
Michael Clayton, CEO of Coperforma, said it had since employed additional staff at its call centres.
South East Coast Ambulance Service, the previous transport provider, said it had "acted professionally throughout the transfer process" and was "very proud of the care provided by our staff over many years".