Yulia Skripal has “responded well to treatment” but her father Sergei remains in a critical but stable condition, Salisbury NHS Foundation Trust said.
The pair were found unresponsive and taken to Salisbury District Hospital after being attacked with nerve agent novichok on 4 March.
Hospital medical director Dr Christine Blanshard said that though Ms Skripal’s condition had improved, she “continues to receive expert clinical care 24 hours a day”.
It comes as officers investigating the attempted murder of the Skripals cordoned off a play area close to their home in Salisbury.
“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,” Met Police deputy assistant commissioner Dean Haydon said.
“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 night, detectives revealed that they believe Sergei and Yulia Skripal 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,” Mr Haydon said.
“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.”
Sky News pictures have since shown Mr Skripal’s house boarded up.
The nerve agent attack has led to increased tensions between the UK and Russia, with Britain accusing Moscow of being behind the attempted murder.
Russia denies any involvement in the attack, which also seriously hurt the first police officer to arrive at the scene.
Dozens of countries have shown support for the UK by expelling Russian diplomats in response.
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Foreign Secretary Boris Johnson said on Wednesday that nations were saying “enough is enough” after “years of vexation and provocation” which had “worn the collective patience to breaking point”.
He said the Kremlin “underestimated the strength of global feeling”, adding: “After all these provocations, this week was the moment when the world decided to say enough to the wearying barrage of Russian lies.”