Lorna Wilkinson, the hospital's director of nursing, said: "While this is welcome news, clearly we are not out of the woods yet".
Russian Federation has committed an attack that resulted in the death of a Briton, defense minister Gavin Williamson said on Monday, linking Russian Federation to the incident after a 44-year-old woman who was poisoned by nerve agent Novichok died.
There is no evidence to suggest they went to any areas that had been decontaminated after the attack on Sergei Skripal and his daughter Yulia, who were exposed to the nerve agent in Salisbury in March.
In a statement on Tuesday, Sturgess's family paid tribute to the late mother of three, calling her "a gentle soul who was generous to a fault".
He said there is so far no forensic proof that the Novichok that poisoned Sturgess and Rowley comes from the same batch used in March against the Skripals - but that any other explanation is extremely unlikely.
They have tested and ruled out a bus on which the pair travelled on Friday night but are still examining a red Transit van in which Mr Rowley travelled on Saturday.
The Skripals fell ill after the poison was applied to the ex-spy's front door in the city of Salisbury.
The two spent weeks in critical condition but have since been discharged from the hospital.
The Kremlin said it was sorry to hear of Ms Sturgess's death but called the suggestion that Russian Federation was involved "absurd".
Britain has blamed Russian Federation for the attack on the Skripals - a charge strongly denied by Moscow which has challenged British authorities to publish the evidence.
It was confirmed on Wednesday by scientists at the UK's chemical laboratory Porton Down that Ms Sturgess and Mr Rowley had been exposed to novichok.
He said no one else in the Amesbury and Salisbury region, where the couple lived in southwestern England, has shown any sign of Novichok poisoning.
The backdrop to this meeting was British but the issue was global as police issued a Novichok warning to the residents of Salisbury.
The auto was seized Monday from a residential street in Swindon, authorities said.
His auto was sealed and taken away on the back of a truck.