Sophie was suffering severe stomach pains

The countess waited 30 minutes to be taken to hospital, after going into labour prematurely on Saturday night.

The inspector - who has not been suspended - was in charge when officers received an emergency call from Sophie's staff at Bagshot Park.

He despatched officers to her home but did not send an ambulance.

Reunited

Police later apologised for the delay, and said the officer in charge mistakenly believed an ambulance had already been called.

The duty inspector has been temporarily moved to desk duties while a full investigation into what happened takes place Surrey Police

Once the error was realised, paramedics were at the countess's home within three minutes and 45 seconds.

The 38-year-old was taken to Frimley Park Hospital, Surrey, where a 4lb 9oz baby girl was delivered one month early, following an emergency Caesarean operation.

The baby was transferred to the neo-natal unit of St George's Hospital, South London, as a precaution but is said to be doing well.

A spokeswoman for the countess said both she and her daughter were continuing to make good progress.

Mother and baby are expected to be reunited on Thursday or Friday.

Surrey Police apologised for causing the countess any distress and said it regretted "getting it wrong".

A spokeswoman said: "The duty inspector has been temporarily moved to desk duties while a full investigation into what happened takes place.

"No one has been suspended over this incident."

Lady Windsor

She added that it was not known how long the investigation would take but said it was being undertaken as a matter of priority. The inspector has not been named.

On Tuesday a palace spokeswoman sought to play down any bad feeling over the handling of Sophie's transferral to hospital, saying: "The Earl did praise all the emergency services after his first visit to the hospital on Sunday."

Prince Edward, who was abroad on an official visit at the time of the birth, flew back to visit both his wife and new daughter on Sunday night.

He visited his wife again on Wednesday lunchtime spending just over an hour at Frimley Park.

The palace said the baby was expected to stay in hospital for two to three weeks.

Sue Macdonald, of the Royal College of Midwives, said medical staff tried to avoid separating mother and child if possible, but said it happened from "time to time".

The birth follows a traumatic failed pregnancy in December 2001 when Sophie was airlifted to hospital after suffering a potentially life-threatening ectopic pregnancy.