Dawn Sturgess, 44, and her 45-year-old partner Charlie Rowley were taken ill on 30 June after coming into contact with the nerve agent used to poison Sergei and Yulia Skripal in Salisbury.
Ms Sturgess died on Sunday evening, while Mr Rowley is still being treated in hospital.
Metropolitan Police Assistant Commissioner Neil Basu said it was a priority to locate a “container” which may have been the “source of the contamination”.
It is believed that Ms Sturgess and Mr Rowley “handled” that container, Mr Basu said.
Though it has not been established whether this incident is linked to the attack on the Skripals, Mr Basu said that theory was the “main line of inquiry”.
There is “no evidence” that either Ms Sturgess or Mr Rowley visited any of the sites that were decontaminated following the attack on the Skripals.
Public Health England is advising people in the area not to pick up items including needles, syringes or unusual containers.
A red transit van that Mr Rowley travelled in the day he fell ill has been identified and taken to Porton Down where tests will be carried out.
Three other men who were also in the van that day have been screened as a precaution, but are not showing any signs of having been exposed to novichok, Mr Basu said.
A further 21 individuals who said they were concerned about possible exposure to novichok have been screened and cleared.
“In the four months since the Skripals and [Detective Sergeant] Nick Bailey were poisoned, no other people besides Dawn and Charlie have presented with symptoms,” Mr Basu said.
“Meticulous” searches are continuing, he added.
“This activity has centred on Dawn’s address at John Baker House, Salisbury, Charlie’s address in Muggleton Road, Amesbury, and Queen Elizabeth Gardens in Salisbury,” Mr Basu said.
“Police cordons are in place at a number of locations in the area and are likely to remain in place for a considerable period of time.”
Detectives have also pieced together a detailed timeline of Ms Sturgess and Mr Rowley’s movements prior to falling ill.
Mr Basu said the death of Ms Sturgess had “only served to strengthen the resolve of our investigation team as we work to identify those responsible for this outrageous, reckless and barbaric act”.
Theresa May paid tribute to Ms Sturgess in the Commons, saying: “I am sure the House will join me in sending our deepest condolences to the family and friends of Dawn Sturgess who passed away last night.
“Our thoughts are also with the people of Salisbury and Amesbury and the Home Secretary will make a statement shortly including on the support we will continue to provide to the local community throughout this difficult time.”