The girls, who were born joined at the liver in Bristol on Thursday, are now in intensive care in adjoining ventilators after the three-hour operation.
A hospital spokeswoman said the condition of the babies, who are not being identified, had been unstable during the operation and they had needed external cardiac massage to restart their hearts. She added that one of the girls was now "stable" while her sister "needed more care".
Surgeon Edward Kiely said: "The operation was not as complex as we anticipated but it is too early to say how the twins will fare."
The separation is the ninth to have been carried out since 1984 by Professor Lewis Spitz, his colleague Mr Kiely and their team at Great Ormond Street, which leads the world in Siamese-twin surgery.
The Spitz-Kiely team has dealt with 12 cases of Siamese twins in the past 14 years and has successfully separated nine. Of those, only three pairs have survived. They include Niamh and Aoife Varley, separated in July last year. The sisters, who were born at St Mary's Hospital in Manchester and now live in Ireland, were born joined at the liver and the chest.
Surgeons were optimistic at the time that the twins would survive because the liver is the only organ capable of regrowth, which meant the two halves could grow back to full size.
In a delicate procedure, the Great Ormond Street team drained the Varley twins' liver of blood then used an ultrasonic cutter to divide it. They then sealed the blood vessels with a natural-based glue. During the operation very little blood was lost.
The twins also shared the pericardial membrane surrounding the heart and major blood vessels. The team overcame that problem by reconstructing the original sac for one twin and making an artificial version for the second.
The other surviving twins are sisters from Italy and brothers who originally came from Sudan but now live in Britain.
Two years ago the hospital's team treated the British Siamese twins Chloe and Nicole Astbury who were born at St Mary's Hospital. They were joined at the breastbone, sharing a liver and bowel. They died from an infection after five weeks, before doctors tried to separate them.
The team also separated Beniaminio and Mario Di Conza, from Italy, in a 10-hour operation, but one of the boys later died.Reuse content