Yulia Skripal is “improving rapidly and is no longer in a critical condition” after she was poisoned with a nerve agent, the hospital has said.
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.”
The pair were found slumped on a bench in Salisbury on March 4, triggering alarm in the Wiltshire town and an international incident between the West and Russia, which is accused of targeting Sergei Skripal, a former double agent.
On Thursday, another cordon went up in the time, this time around a child’s play area near the Skripals’ home.
In a statement, Scotland Yard said: “Officers investigating the attempted murders of Sergei Skripal and his daughter Yulia Skripal are continuing to focus their enquiries around the Skripals’ home address.
“As a precautionary measure, they have this afternoon placed a cordon around a children’s play area at Montgomery Gardens, near the Skripals’ home.”
Deputy Assistant Commissioner Dean Haydon said: “I would like to reassure residents that we have placed the cordons around the park, and officers will be searching it, as a precautionary measure.
“I would like to reiterate Public Health England’s advice that the risk to the public is low. Anyone with concerns regarding the ongoing police activity in Salisbury is encouraged to speak to the local officers or PCSOs at the locations, who will be happy to offer reassurance.”
On Wednesday, investigators announced they believed the Skripals first came in to contact with Novichok, the agent they were poisoned with, on the front door of Skripal’s home in Salisbury.
His niece Viktoria Skripal has told the BBC the family shielded his 90-year-old mother from the news.
“The first priority was to protect our granny so that she wouldn’t hear or find out anything,” she said, adding there was a slim chance the pair would survive the March 4 attack, saying the prognosis “really isn’t good”.
“Out of 99%, I have maybe 1% of hope. Whatever it was has given them a very small chance of survival. But they’re going to be invalids for the rest of their lives,” Viktoria Skripal told the BBC.
On Tuesday, Theresa May told parliament that the Skripals may never recover from what happened.
She told MPs: “Late last week, doctors indicated that their condition is unlikely to change in the near future, and they may never recover fully.
“This shows the utterly barbaric nature of this act, and the dangers that hundreds of innocent citizens in Salisbury could have faced.”
Cordons have gone up in Salisbury at places the Skripals visited, including a Zizzi’s restaurant and a pub.
May said 130 people could have potentially been exposed to the nerve agent.
He said: “People ask me how I am feeling – but there are really no words to explain how I feel right now. Surreal is the word that keeps cropping up – and it really has been completely surreal.
“I have been so very overwhelmed by the support, cards and messages I have received – everyone has been so incredible.”