She and her boyfriend, Charlie Rowley, 45, were admitted June 30 after falling ill a few kilometres away in Amesbury; Rowley remains in critical condition.
"This awful news has only served to strengthen our resolve to identify and bring to justice the person or persons responsible for what I can only describe as an outrageous, reckless and barbaric act", said Neil Basu, chief of the Metropolitan Police's counter-terrorism division.
"We are not in a position to say whether the nerve agent was from the same batch that the Skripals were exposed to", they said.
Police in HAZMAT suits as they investigate the poisoning of two people in Salisbury.
Russia, now hosting the soccer World Cup, has denied any involvement in the March incident and suggested the British security services carried out the attack to stoke anti-Moscow hysteria.
Sturgess leaves behind three children.
"Police and security officials are working urgently to establish the facts of this incident, which is now being investigated as a murder", the statement read.
"The Government is committed to providing full support to the local community as it deals with this tragedy", she wrote in a second tweet.
Calls for ban on bouncy castles after child dies in Norfolk
Crowds had flocked to Gorleston, a popular beach destination for families, as the area was experiencing a heat wave. The death is the latest in which a fun day out involving a giant inflatable has turned to tragedy.
The 67-year-old ex-agent was living in Salisbury, a cathedral city 145 kilometres southwest of London, when he was struck down along with his daughter, Yulia, who was visiting him.
Meanwhile the investigation into the attempted murders of the Skripals is ongoing as detectives continue to assess all the evidence available.
The poisoning of the Skripals, both of whom spent weeks in hospital before being discharged, was blamed by the United Kingdom government on Russian Federation.
On Twitter, Prime Minister Theresa May said she was "appalled and shocked" by Sturgess' death.
The hospital's medical director, Christine Blanshard, told the BBC that hospital staff worked tirelessly to save Sturgess.
Authorities later determined that both people had been exposed to Novichok, a military-grade nerve agent produced by the Soviet Union decades ago.
He said: "Ms Sturgess was an innocent member of the public who should have been able to go about her daily life without becoming an unwilling victim in such an unprecedented, international, incident".
Moscow hit back by expelling Western diplomats.
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.