The Countess had to have a full transfusion after losing pints of blood during three hours of surgery and sources said yesterday that it had been “touch and go” for both mother and baby at one point.

The Countess was “very, very weak and barely conscious” for the first few days, sources said. She was kept heavily sedated because of the pain she was in, although she was now recovering.

Because of the seriousness of her condition, only her husband and parents have so far been allowed to visit her. The Queen has, however, been kept closely informed of the progress of both mother and baby, who was born prematurely, weighing 4lb 9oz.

The Countess had been distraught on Thursday to learn that she would not be well enough to leave hospital until after the weekend. Friends said she was desperate to see her daughter. Although she had held her baby immediately after the birth, it is understood that she had no recollection of this at all, and was having to make do with looking at photographs taken by nurses.Yesterday, however, the baby was taken from St George’s Hospital, Tooting, to her mother at Frimley Park Hospital, after discussions between St George’s, royal doctors, the Queen and the Duke of Edinburgh.

The Earl of Wessex was with his wife and daughter for the reunion and he later said it was a fantastic day. Palace sources described the reunion as highly emotional and moving. “There were tears from both the Countess and the Earl,” one said.

The Earl said afterwards that his daughter, who is eighth in line to the throne and has yet to be named publicly, could be in hospital for weeks. “She’s out of intensive care, but she’s premature, so they have to monitor her very carefully,” he said. His remarks were the first official indication that Buckingham Palace had initially played down the seriousness of his wife and daughter’s conditions.

Thanking the “absolutely brilliant” staff at both hospitals, the Earl added: “This has been a fantastic day, a day of great relief and joy. It’s difficult to explain what it is to be together as a family for the first time. The amazing thing is that our baby girl has been able to recover well enough that she can come here to join Sophie, which is fantastic.”

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