“Yulia has asked for privacy from the media and I want to reiterate that request,” Dr. Christine Blanshard, medical director of Salisbury District Hospital, told reporters on Tuesday. “This is not the end of her treatment, but marks a significant milestone.”
Though Mr. Skripal, 66, “is recovering more slowly than Yulia,” Dr. Blanshard said, “we hope that he, too, will be able to leave hospital in due course.”
She did not comment on reports in the British news media that Ms. Skripal, 33, was released on Monday. It was not immediately clear where Ms. Skripal might go; investigators have sealed off Mr. Skripal’s house in Salisbury, and investigators say the nerve agent was most likely applied to its front door.
One other person is known to have been sickened by the toxin, Detective Sergeant Nick Bailey, who went to the house at the start of the investigation. He was released from the hospital on March 22.
Ms. Skripal, who lives in Russia, was visiting her father when they were poisoned, and it is not clear whether she will return.
Russian officials say they have been improperly denied access to her, but the British police said last week that Ms. Skripal was aware of the Russian offer to visit and help, and that she had turned it down.
On Tuesday, the Russian Embassy in London wrote on Twitter: “We congratulate Yulia Skripal on her recovery. Yet we need urgent proof that what is being done to her is done on her own free will.”
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The case has mixed high-stakes international diplomacy with elements of farce. Hundreds of diplomats around the world have been expelled, Britain has moved to crack down on the financial dealings of Russians in the country, and President Vladimir V. Putin’s government has offered a variety of alternative explanations for what happened and complained that the Skripals’ pets — two guinea pigs and a cat — were killed by the British and then cremated to destroy evidence.
The investigation took another bizarre twist last week when Viktoria Skripal, a 45-year-old Russian accountant and relative of the two Russians, questioned the accounts of the British authorities and said that she was “scared” for the pair.
She made her comments in an interview, conducted after she recorded what she said was a phone call with Yulia Skripal. She then gave the recording to Russian state television, which broadcast it.
The Organization for the Prohibition of Chemical Weapons, an international body, is examining evidence in the case and is expected to announce the results of its tests this week. The findings of its investigation are expected to be limited, however, to identifying the poison but not its source.
Weeks ago, British government officials speculated that the Skripals might never fully recover.
On Tuesday, Dr. Blanshard offered her most detailed public account of the danger and treatment they had faced.
“Nerve agents work by attaching themselves to a particular enzyme in the body, which then stops the nerves from working properly,” she said. “This results in symptoms such as sickness, hallucinations and confusion.”
“Our job in treating the patients has been to stabilize them, ensuring that the patients could breathe and that blood could continue to circulate,” she added. “We then needed to use a variety of different drugs to support the patients until they could create more enzymes to replace those affected by the poisoning. We also used specialized decontamination techniques to remove any residual toxins.”
Mr. Skripal, an officer in Russian military intelligence, was convicted in 2006 of selling secrets to the British, and was imprisoned. In 2010, he was sent to Britain as part of a spy swap, and he has lived in England since.
It was not clear why Russian officials — or anyone else — would have targeted him, but experts say the poisoning has sent a powerful message to Russians living in the West that they are never out of the Kremlin’s reach.
In 2006, another former Russian spy, Alexander V. Litvinenko, was fatally poisoned in London with a radioactive element, polonium 210, an assassination that Britain contends was directed by Moscow, which Russia denies. Since then, several Putin critics and their associates have died under suspicious circumstances in Britain, and British officials have vowed to re-examine those cases.