They are said to have claimed that their child had been born at the nearby Royal London Hospital in nearby Whitechapel on March 1 before being transferred.
They are then believed to have shown staff a photo of 'their baby' in an incubator - thought to be a printout from the internet and said they had come to collect their child from the neo-natal unit. Staff are understood to have checked with bosses at the Royal London Hospital for premature babies being born on March 1, but found no records and alerted the police.
Officers arrived at the scene and a man and a woman were arrested on suspicion of conspiracy to abduct a child.
The couple have now been released on bail on the condition that they should not enter any hospital - unless they are suffering a 'medical emergency'.
Inspector Paul Clarke, of the Met Police, said: 'The actions of the staff at Great Ormond Street Hospital in making all of the necessary checks and the quick response of police in arresting a couple prevented what could have been a very frightening and harrowing incident.'
A spokeswoman for Great Ormond Street Hospital said: 'Thankfully, this type of incident is exceptionally rare.
'We are pleased that staff at the hospital acted so swiftly and calmly to ensure the safety of all our patients.'