Dawn Sturgess, 44, from Amesbury, eight miles north of Salisbury, fell ill on 30 June, and died on Sunday after she was exposed to "a large dose" of the substance, while her partner, Charlie Rowley, remains critically ill in hospital.
Today, Ms Sturgess" family said her death on Sunday had been "devastating' for them.
British Home Secretary Sajid Javid said scientists have yet not determined if the nerve agent that caused Sturgess' death was from the same batch that poisoned the Skripals.
"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", the statement said, according to BBC News.
The Sturgess family added: "Our thoughts and prayers also go out to Charlie and his family and we wish Charlie a speedy recovery".
"The simple reality is that Russian Federation has committed an attack on British soil which has seen the death of a British citizen", Williamson said.
"That is something that I think the world will unite with us in actually condemning".
Police have launched a murder inquiry following the death of Ms Sturgess at Salisbury District Hospital, after concerns the pair were exposed to novichok through a contaminated item left over from the attack on the Skripals.
Dawn was from Salisbury and was taken ill at her partner Mr Rowley's flat in nearby Amesbury.
Britain blamed the Russian state for the attack on Sergei Skripal and his 33-year-old daughter - an allegation Moscow has repeatedly denied.
The Ministry of Defence is working with the police on the investigation and the clear-up effort, with 175 armed forces personnel involved. The three of most interest are Queen Elizabeth Gardens in Salisbury, where the British couple spent part of Friday; the Salisbury homeless hostel where Sturgess lived and both visited on Friday; and Rowley's Amesbury home.
"It was subsequently taken to DSTL and following further scientific advice, the investigation team also carried out forensic enquiries on the bus as they look to establish the point at which Dawn and Charlie were contaminated with the nerve agent".
Javid, who is chairing a meeting of the government's emergency committee on Monday, has said there were no plans at this stage for further sanctions against Russian Federation.