Update - 3.24pm: Yulia Skripal is "improving rapidly and is no longer in a critical condition. Her condition is now stable".
Her father Sergei remains in a critical but stable condition, Salisbury NHS Trust said.
Dr Christine Blanshard, medical director for Salisbury District Hospital, said: "I'm pleased to be able to report an improvement in the condition of Yulia Skripal.
"She has responded well to treatment but continues to receive expert clinical care 24 hours a day.
"I want to take this opportunity to once again thank the staff of Salisbury District Hospital for delivering such high-quality care to these patients over the last few weeks.
"I am very proud both of our front-line staff and all those who support them."
9.21am: Deadly nerve agent in highest concentration on ex-spy's front door, tests reveal
A former Russian spy and his daughter who were victims of a nerve agent attack first came into contact with the deadly chemical at his home, police said.
Ex-spy Sergei Skripal and his daughter Yulia remain in a critical condition in hospital following the Novichok poisoning on March 4 in Salisbury, Wiltshire.
Detailed forensic testing revealed the highest concentration of the nerve agent was found on the front door of Mr Skripal's home in Christie Miller Road, in Salisbury.
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The Metropolitan Police said traces of the nerve agent had been found at some of the other scenes detectives have been working at, but at lower concentrations.
Detectives will now focus their inquiries in and around the address, and specialist teams will step back from some of the other areas investigated over the past few weeks.
Deputy assistant Commissioner Dean Haydon, senior national co-ordinator for counter-terrorism policing, said: "At this point in our investigation, we believe the Skripals first came into contact with the nerve agent from their front door.
"We are therefore focusing much of our efforts in and around their address. Those living in the Skripals' neighbourhood can expect to see officers carrying out searches as part of this, but I want to reassure them that the risk remains low and our searches are precautionary."
He thanked members of the public for their understanding, adding that officers will likely be in the neighbourhood for several months.
Britain has accused Russia of being behind the poisoning - allegations fiercely denied by Moscow.
In turn, Russia has suggested that UK intelligence officers may have been involved in the poisoning.
The Kremlin allegation came as Moscow faced increasing global isolation, with at least 26 countries expelling a total of more than 130 suspected spies.
Britain insists there is no plausible alternative explanation for the attack, and has dismissed the series of suggestions emanating from Moscow as nonsense.
Around 250 counter-terrorism detectives continue to work around the clock on the investigation, which is expected to continue for months.
Officers are examining more than 5,000 hours of CCTV footage and 1,350 exhibits that have been seized, while 500 witnesses have been identified.
The London Road cemetery, where his wife and son are buried, the Maltings shopping centre where Mr Skripal and his daughter were discovered unconscious, and the Ashley Wood compound have been handed back into the control of Wiltshire Police.