More than 240 witnesses have been identified as police investigate the Russian ex-spy poisoning "at speed", the home secretary has said.
Amber Rudd praised the professionalism of the police who are now looking at more than 200 pieces of evidence.
The investigation into the attempted murder of Sergei Skripal and his daughter Yulia is now in its sixth day.
Meanwhile, Det Sergeant Nick Bailey, who fell ill attending the pair, has denied he is a "hero".
Mr Bailey remains seriously ill but is awake and engaging with his family.
Ms Rudd said both Col Skripal, 66, and his daughter, 33, who are being treated at Salisbury District Hospital, remain in a "critical but stable condition" after being exposed to a nerve agent.
The pair were found unconscious on a bench in Salisbury, Wiltshire, on Sunday 4 March.
More than 250 counter terrorism police are now involved in what the home secretary has described as a "major investigation".
"The police have said that if anybody thinks they have any additional information they would welcome them coming forward.
"There is also substantial amounts of CCTV they have to go through. This is a painstaking, detailed investigation and the police need to be given the space and time to get on with it."
Mr Skripal was convicted by the Russian government of passing secrets to MI6, but given refuge in the UK in 2010 as part of a "spy swap".
Russia has denied any involvement. UK Foreign Secretary Boris Johnson has said the country will respond "robustly" if Moscow is found to have been behind the incident.
Alexander Skripal died aged 43 last July in St Petersburg from liver failure, and his mother died of cancer in 2012.