The twin girls were born by Caesarean section at St Michael's Hospital in Bristol on Thursday afternoon.
Paediatric surgeon Professor Lewis Spitz and Mr Edward Kiely, consultant paediatric surgeon, were preparing for the eight-hour operation.
"There is no information at this time about specific details of the surgery. No two conjoined twin separations are the same and, as always, they are very complex and delicate operations," a Great Ormond Street spokesman said.
"The twins have been admitted to an intensive care ward here for an assessment of their condition and preliminary investigations have already been undertaken."
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