"We remain committed to making our service with our partner Harmoni a success, " she added.
BBC: NHS postpones West region out-of-hours GP helpline launch
Dr Lee said after the death the Harmoni centre carried out an "exceptionally detailed" review of the circumstances.
Harmoni said the launch of the new number had created some areas where it had yet to achieve high levels of service.
BBC: NHS postpones West region out-of-hours GP helpline launch
Ambulance unions say patients are therefore often being advised to dial 999 instead and in some cases Harmoni call-handlers are sending ambulances themselves.
The NHS said it would work with service operator Harmoni to ensure it is delivered to a satisfactory level "as soon as possible".
BBC: NHS postpones West region out-of-hours GP helpline launch
But there are concerns that Harmoni's call handlers are not medically trained and there are not enough doctors to cover the area at busy times.
During the hearing, Dr Muttu Shantikumar of the Harmoni centre said he set the baby's appointment as "routine" and the one he arranged was the earliest available.
Linda Peanberg King, of Islington, north London, told St Pancras Coroner's Court she went to her GP once and the private Harmoni centre twice, after seven-week-old Axel fell ill.
BBC: Islington baby died despite doctor visits, inquest hears
Axel's mother Linda Peanberg King, of Islington, north London, told the inquest she went once to her GP and twice to the Harmoni centre at the Whittington Hospital in Archway, after Axel fell ill last October.
In a statement Harmoni said the launch of the new number had created some areas where they had yet to achieve the high levels of service they will meet over time and they were working to address these issues.
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