The possibility that the two investigations might be linked is "clearly a key line of inquiry for police", the Met said.
Britain and its allies blamed Moscow for trying to kill the pair, prompting angry denials that led to an global diplomatic crisis.
Britain has blamed Putin's government for the poisoning of the Skripals, which triggered a diplomatic row in which Britain and its allies expelled more than 150 Russian diplomats.
Home Secretary Sajid Javid said the area is open for business and urged people to visit what he called one of the most attractive parts of the country.
Dawn Sturgess, 44, died on Sunday evening in hospital.
A police officer sought medical advice Saturday in connection with the ongoing investigation of the nerve agent exposure, but was given the "all clear", according to Wiltshire Police.
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The Britons were initially thought to have taken an overdose of heroin or crack cocaine. They had been exposed to an agent known as Novichok. While Russia made a point previous year of destroying its last remaining stockpiles of publicly declared chemical weapons, Reuters noted that it is "not believed to have ever declared Novichok or its ingredients to the Hague-based Organisation for the Prohibition of Chemical Weapons (OPCW)".
The Defence Science and Technology Laboratory at Porton Down confirmed on Wednesday that the victims had been exposed to Novichok.
"At any case, we believe it would be quite absurd", said the Kremlin spokesman.
Both the Skripals have now been released from hospital and are living in a secret location.
Britain blames the Russian state for the attack on Sergei Skripal and 33-year-old Yulia - an allegation Moscow has repeatedly denied. Her father was discharged on May 18.
The question for officials is whether they want to be more direct in their challenge to Russian Federation now Ms Sturgess has died and anger is growing, or whether they will still wait to collect more evidence. Neighbours said they did not know who the van belonged to.
Her mother said the 44-year-old, who had alcohol and addiction problems, had suffered heart failure after more than a week in intensive care.
Police and public health officials insist the risk to the wider public remains low.