More than 240 witnesses have been identified as police investigate the Russian ex-spy poisoning at speed.
Home secretary 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”.