A police officer who was part of the initial response to the incident is also in a serious condition
British police believe a nerve agent was used to try to murder a former Russian double agent and his daughter.
Sergei and Yulia Skripal were found unresponsive on a bench in the Wiltshire city on Sunday.
The pair - who are aged in the 60s and 30s respectively - remain in a criticial condition in intensive care, police say.
Health officials in the UK have stressed that the risk to the public is low.
However, one police officer who was part of the initial response to the incident is in a serious condition.
AC Rowley: “If you're feeling unwell & think you may have been in the area where this happened please seek medical advice, but we’d like to reiterate we're not seeing any evidence of a wide spread health issue. We're also working with agencies to ensure public safety & wellbeing”— Metropolitan Police (@metpoliceuk) March 7, 2018
Counter-terrorism police in London have taken the lead in the investigation, and provided an update this afternoon.
In a statement, Met Police said: "This is being treated as a major incident involving attempted murder by the administration of a nerve agent.
"We believe the two people who originally became unwell were the specific targets and are focused on identifying and finding those responsible."
A number of areas remain closed off following the incident on Sunday.
Police say CCTV is being reviewed 'as a matter of urgency', while officers are said to be working around to clock as part of efforts to solve the mystery.