It is understood Dr Shakoor has been transferred to the Broomfield to be closer to his daughter. He is said to be traumatised.
Essex Police are treating the blaze as suspected arson and there is evidence that some form of accelerant was used.
A spokesman for the force said: "The cause of the fire is still under investigation and detectives cannot rule in or rule out all lines of inquiry and cannot speculate on the motive or cause."
Dr Shakoor worked at the Princess Alexandra Hospital. Dr Usmani did not work as she cared for the children. Originally from Karachi, Pakistan, they lived in Saudi Arabia, where the children were born, for more than a decade before moving to the UK.
Witnesses should contact the major investigation team at Harlow on 101.