But he said health authorities continued to assert the risk to the public was low.
"It is both shocking and utterly appalling that a British citizen has died having been exposed to a Novichoknerve agent but make no mistake we are determined to find out how Dawn and her partner Charlie came into contact with such a deadly substance", Basu said.
"Dawn will always be remembered by us as a gentle soul who was generous to a fault", the statement read.
"She would do anything for anybody and those who knew Dawn would know that she would gladly give her last penny to somebody in need".
"Our thoughts and prayers also go out to Charlie and his family and we wish Charlie a speedy recovery", the family said.
Dr Christine Blanshard, from Salisbury District Hospital, where Ms Sturgess was treated, described her death as "desperately sad" and sent her condolences to the family.
The 67-year-old ex-agent was living in Salisbury, a cathedral city 90 miles (145 kilometers) southwest of London, when he was struck down along with his daughter, Yulia, who was visiting him.
One line of inquiry suggests that after the Skripals were attacked by the nerve agent, the assailants disposed of vials, ampules or a mixing kit - or some other contaminated items - and that Rowley and Sturgess found the material and were accidentally exposed.
A forensics officer wearing protective equipment investigates at a public housing site in Salisbury on July 6 after the hospitalization of Dawn Sturgess and Charlie Rowley.
Home Secretary Sajid Javid said the area is open for business and urged people to visit what he called one of the most handsome parts of the country.
Javid said earlier on Sunday that police had a working hypothesis that the two poisoning incidents were connected.
After the Skripal poisoning in March, British Prime Minister Theresa May concluded that it was "highly likely" Russia was responsible for the attack, "b$3 ased on the positive identification of this chemical agent; ...our knowledge that Russia has previously produced this agent and would still be capable of doing so; Russia's record of conducting state-sponsored assassinations; and our assessment that Russia views some defectors as legitimate targets for assassinations". Still, more than 20 other countries have expelled Russian diplomats in a show of support for the UK.
March 22: Det. -Sgt.
The Skripals both survived despite extended stays in hospital.
March 26: European Union countries and others including Canada show solidarity with the U.K.by expelling Russian diplomats. Russian Federation responds with its own banishments of foreign diplomats.
Over the weekend a police officer took himself to Great Western Hospital in Swindon over concerns of novichok poisoning. For its part, Russian government officials have denied all involvement, while at least some British officials have urged caution in attributing blame.
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