Met Police counter terrorism officers have extended cordons in the city.
A bridge was shut on Tuesday evening, while Salisbury's Zizzi restaurant and The Bishop's Mill pub remain sealed off.
Mr Skripal and his daughter were found slumped and unconscious on a bench outside the Maltings shopping centre on Sunday afternoon.
The Cobra meeting will be chaired by Home Secretary Amber Rudd. The cross-departmental committee meets to examine government responses to national emergencies.
Scotland Yard, which took over the investigation from Wiltshire Police on Tuesday, said it was keeping an "open mind" and the case had not been declared a terrorist incident.
Assistant Commissioner Mark Rowley said: "This investigation is at the early stages and any speculation is unhelpful...
"We would like to reassure members of the public that this incident is being taken extremely seriously and we currently do not believe there is any immediate risk to the wider public."
BBC Newsnight's diplomatic editor Mark Urban said scientists at Porton Down have still not identified the substance the pair are thought to have been exposed to, with one official saying they were being treated for "symptoms rather than causes".
Prof Alastair Hay, from the University of Leeds, said test results could take several days.
He said: "Individuals cannot provide unlimited amounts of blood for testing so investigations will be guided by the clinical team."
Two police officers caught up in the suspected contamination were treated in hospital for minor symptoms, before they were given the all clear.
It is understood their symptoms included itchy eyes and wheezing.
A third member of the emergency services remains in hospital.
Relatives of Col Skripal, who was convicted in Russia in 2006 of spying for Britain, have told the BBC Russian Service that he believed the country's special services might come after him at any time.
His wife, elder brother and his son have died in the past two years, some in mysterious circumstances, the family believes.
Ms Skripal lives in Moscow and has visited her father in the UK regularly, especially during the past two years.
On Tuesday, Foreign Secretary Boris Johnson told MPs the UK would respond "robustly" to any evidence of Russian "state responsibility" in the case.
He said that could include sanctions and asking UK dignitaries not to attend the World Cup in Russia this summer.
The foreign secretary said he was not pointing fingers, but described Russia as "a malign and disruptive force".