Yulia Skripal, daughter of former Russian double agent Sergei Skripal, has spoken publicly for the first time since the pair were poisoned with a nerve agent.

The 33-year-old said she regained consciousness more than a week ago and has been recovering well since then.

“I woke up over a week ago now and am glad to say my strength is growing daily. I am grateful for the interest in me and for the many messages of goodwill that I have received,” Ms Skripal said in a statement released on her behalf by London’s Metropolitan Police.

“I have many people to thank for my recovery and would especially like to mention the people of Salisbury that came to my aid when my father and I were incapacitated. Further than that, I would like to thank the staff at Salisbury District Hospital for their care and professionalism,” she said.

“I am sure you appreciate that the entire episode is somewhat disorientating, and I hope that you’ll respect my privacy and that of my family during the period of my convalescence.”

The development comes as the United Nations Security Council meets to discuss the spiralling diplomatic crisis sparked by the poisoning.

The Skripals were found slumped on a bench in the southern English city of Salisbury on March 4 in a nerve agent attack that the British government has blamed on Russia, with what it says was a military-grade Novichok nerve agent.

Hospital bosses said her father, Sergei, was still in a critical but stable condition in an intensive care unit.

‘I am sure she will return to Moscow’: Ambassador

Russia’s ambassador to Britain Alexander Yakovenko said he was happy to hear that Ms Skripal was recovering.

Russia denies any involvement but the crisis has led to the worst diplomatic crisis between Russia and Western nations since the Cold War.

Mr Yakovenko was part-way through a news conference at his official residence in London when Ms Skripal’s statement was issued.

Asked about the statement by a reporter, Mr Yakovenko said: “I am really happy and I hope that Sergei Skripal will also recover. I am quite sure that one day Yulia will come back to Moscow.”

Russian ambassador to the UK Alexander Yakovenko. Photo: AAP

Earlier on Thursday, Russian state TV and Interfax reported that Ms Skripal had phoned her cousin Viktoria Skripal in Russia, saying she and her father were both recovering and that she expected to leave hospital soon.

“Everything is fine, everything is fixable, everyone is getting better, everyone is alive,” they quoted her as saying in the call.

When asked about her father’s health, Ms Skripal was cited by them as saying: “Everything is fine, he is resting right now, sleeping. Everyone’s health is fine, nobody has any problems that can’t be put right. I will soon be discharging myself [from hospital].”

Russian state TV said it could not vouch for the authenticity of the quotes.

Viktoria Skripal, Mr Skripal’s niece, has said she plans to travel to England and try to bring Ms Skripal back to Russia.

Russia this week called a meeting of the global chemical watchdog over the Salisbury incident, but failed in its bid to join the probe by the Organisation for the Prohibition of Chemical Weapons (OPCW).

-with AAP