Sophie is said to be "stable" but must stay in hospital

The countess is said to be making good progress in a Surrey hospital after an emergency Caesarean on Saturday night.

Her daughter, described as stable, is in a hospital in south London.

Surrey Police were alerted when Sophie began suffering cramps, but did not call an ambulance as they thought one had already been requested.

Newspaper reports said the error was not realised for 30 minutes.

When the ambulance did arrive, the 38-year-old countess was rushed five miles from her home in Bagshot Park, Surrey, to Frimley Park Hospital, where doctors carried out the operation.

A spokesman for Surrey Police said: "A call was received at 21.59 [GMT] on Saturday by Surrey Police call handling centre from Bagshot Park security.

"The call was passed to the duty inspector who believed that an ambulance had already been called because of the way in which the message was recorded.

'Distress'

"He immediately put into effect the security operation surrounding the call of an ambulance and despatched police response within one minute. An ambulance was not called.

Edward said meeting his daughter was "thrilling"

"Surrey Police recognises we got it wrong and are apologising to the royal couple for any distress the Countess of Wessex suffered due to the delay."

The matter was being investigated so that lessons could be learned in the future, the spokesman said.

Both Sophie and her baby daughter are making good progress, Buckingham Palace said on Tuesday.

The Palace added the baby was expected to stay in hospital for two to three weeks, while Sophie is not expected to be discharged from the NHS Frimley Park Hospital in Surrey before Thursday or Friday.

The 4lb 9oz baby, who has so far not been named, was born a month early after the countess became ill.

She was transferred to a neo-natal unit at St George's Hospital in south London immediately after the operation "as a precaution".

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.

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

I am rather shocked at the moment but delighted, just thrilled to bits Earl of Wessex

Visiting his daughter on Monday, Prince Edward said the experience of being a father was "thrilling".

"It was a completely thrilling moment, quite difficult to describe.

"Obviously she is very small at the moment but she's cute and cuddly. But I would say that because I'm the father," he told reporters.

'Avoid separation'

Sue Macdonald of the Royal College of Midwives said medical staff tried to avoid separating mother and child if possible, as it could prove "traumatic".

"It does happen from time to time, especially when there isn't a neonatal unit on site. It's not rare, but it is something we try to avoid if we can," she said.

Overall there shouldn't be any long-term effects from the separation Sue Macdonald, Royal College of Midwives

"To help them, we try and limit any separation, and get photos of the baby for the mother. Some units even have video links so the mum can see what her baby is up to."

But she added: "Overall there shouldn't be any long-term effects from the separation."