Police said they were continuing to investigate how Dawn Sturgess and a 45-year-old man, named by media as Charlie Rowley, came across an item contaminated with Novichok, which was developed by the Soviet military during the Cold War.
"This is shocking and tragic news", Neil Basu, of the UK's counterterrorism agency, said. May also said her "thoughts and condolences" go to Sturgess' family and loved ones.
More than 100 police are trying to search all areas where Sturgess and Rowley had been before they became ill.
Tests have confirmed that it was the same type of Novichok used to poison the Skripals, he said, and that Rowley and Sturgess "touched a contaminated item with their hands".
However, Russian authorities have repeatedly denied any involvement.
British Home Secretary Sajid Javid was chairing a meeting of the government's Cobra emergencies committee and was later due to update MPs in the House of Commons.
"I simply can not offer any guarantees", said Assistant Commissioner Neil Basu, who is leading the investigation. They say the poison could remain potent for months, particularly in a closed container.
Assistant Commissioner Neil Basu, the head United Kingdom counter-terrorism policing which is leading the investigation, said he was "unable to say" if the incident in Amesbury is linked to the poisoning of the Skripals on 3 March - but it is their "main line of inquiry".
Detectives are still working to determine the source of the contamination.
Salisbury District Hospital's medical director, Dr. Christine Blanshard, said the staff "worked tirelessly to save Dawn".
The Kremlin said it would be "absurd" to suggest Russian Federation was involved in the death of Sturgess.
But he said health authorities continued to assert the risk to the public was low.
They are not showing any signs of having been exposed to the nerve agent, and are being screened as a precaution.
The Skripals were released from hospital but the investigation into the attack on them continues.
Russia, which is now hosting the football World Cup, has denied any involvement in the Skripal case and suggested the British security services had carried out the attack to stoke anti-Moscow hysteria.
The couple were found unconscious at a house in Amesbury town of Wiltshire.
But when asked directly if Russian Federation was responsible for the latest poisonings, he said it was hard to see any "other plausible explanation".
The police officer added: "The investigation must be led by the evidence available and the facts alone". "It is more of a British issue and the question is to what extent Great Britain is interested in conducting a real investigation", he noted.
Per CNN, authorities now believe that Sturgess and Rowley came into contact with a contaminated item via their hands, but now lack the ability to determine whether the poison is from the same batch that the Skripals ingested.