"He is in a critical but stable condition and is now conscious", the hospital said in a statement on Tuesday.
Dawn Sturgess and Charlie Rowley, were found unconscious.
She is believed to have touched an item contaminated with Novichok, the poison used in a failed attempt to assassinate former Russian spy Sergei Skripal, 67, and his daughter Yulia, 33, in March. Then London pinned all the blame on Moscow, but Russian Federation repeatedly refuted all allegations about its involvement in the incident. Rowley and his partner, Dawn Sturgess, handled the small container made of glass, plastic or metal, which led them to fall ill on Saturday.
The UK's chief medical officer Dame Sally Davies has warned members of the public in Salisbury and Amesbury not to pick up "any foreign objects".
When asked if Basu was looking for a "needle in a haystack" and he said, "That's why we need witnesses or intelligence", Sky News reports.
"Dawn will always be remembered by us as a gentle soul who was generous to a fault", the family wrote.
Mr Rowley has regained consciousness and is in a serious but stable condition in hospital.
Six locations visited by the couple have been cordoned off, including Mr Rowley's home on Muggleton Road in Amesbury, a Boots shop and a baptist church.
They had both been taken to hospital in the city of Amesbury on June 30.
The investigation became a murder hunt after the death of Sturgess, a 44-year-old mother of three, who lived in Amesbury, a town near Salisbury.
Police seized a vehicle in Swindon on Monday as part of their ongoing investigation into the poisoning.
The company shared photographs of their "Novichok" vodka to their Facebook page on July 7, one week after Ms Sturgess and her partner were rushed to hospital after being posioned.
Local residents said the paramedic had told them he got bodily fluids on him, but he had been checked over by doctors and given the "all-clear".
It was feared it might have been contaminated and was taken to the Government laboratory at Porton Down, near Salisbury, to be destroyed.
Britain's public health authority acknowledged on Friday the concerns of people living in the area after the two incidents involving Novichok, but said it was confident that the risk to the public remained low.