Prime Minister Theresa May said she was "appalled and shocked" by the death of Sturgess, according to the BBC.
The woman, 44-year-old Dawn Sturgess, died Sunday in a Salisbury hospital in western England, after collapsing just over a week ago on June 30.
Sturgess and a 45-year-old man both took ill at a residential address in Amesbury on June 30.
Rowley, 45, remains critically ill in hospital.
The Met Police have now confirmed further tests of samples from Dawn and Charlie Rowley show they were exposed to the nerve agent after touching a contaminated item with their hands.
A middle-aged British woman, who somehow came into contact with the Soviet-era nerve agent, died Sunday evening in a hospital in south England where she was being treated for exposure to the chemical weapon.
Neil Basu leads counter-terrorism efforts for the Metropolitan Police force.
"Detectives will continue with their painstaking and meticulous work to gather all the available evidence so that we can understand how two citizens came to be exposed with such a deadly substance that tragically cost Dawn her life", he said.More news: World Cup big guns primed for last-eight battles
"The possibility that the two investigations might be linked is clearly a key line of inquiry for police".
Britain has openly accused Russian Federation of being responsible for poisoning the Skripals with Novichok, a family of advanced nerve agents developed by the Soviet Union in the 1970 and 1980s.
"Police and security officials are working urgently to establish the facts of this incident, which is now being investigated as a murder", she said.
The hospital's medical director, Christine Blanshard, told the BBC that hospital staff worked tirelessly to save Sturgess.
The British couple were believed to have become exposed to Novichok by handling a "contaminated item", with speculation that it could have been the container used to administer the nerve agent to the Skripals. Sturgess was taken to hospital around 10.15am and Rowley several hours later, around 3.30pm.
But he said health authorities continued to assert the risk to the public was low.
Yulia Skripal, Sergei's daughter, was in a coma for 20 days after she was attacked and was eventually discharged about five weeks after the poisoning. Police said there is no evidence that either Sturgess or Rowley visited any of the sites where the Skripals may have been poisoned.