Mr Skripal, 66, and his daughter Yulia, 33, have been in hospital for more than a month after being found unconscious on a bench in Salisbury. They had been poisoned with a toxic nerve agent called Novichok. Ms Skripal is conscious and talking in hospital.
Dr Christine Blanshard, medical director at Salisbury District Hospital said: "Last Thursday, I informed you that Yulia Skripal's condition had improved to stable.
"As Yulia herself says, her strength is growing daily and she can look forward to the day when she is well enough to leave the hospital.
"Any speculation on when that date will be is just that - speculation.
"In the meantime, Yulia has asked for privacy while she continues to get better - something I'd like to urge the media to respect."
Dr Blanshard added: "I also want to update you on the condition of her father, Sergei Skripal. He is responding well to treatment, improving rapidly and is no longer in a critical condition."
Following the update on Mr Skripal's condition, the Russian Embassy tweeted: "Good news!"
Former double agent Mr Skripal, who was jailed by Russia for spying for Britain's intelligence service but released as part of a spy swap between the US and Russia in 2010, was being visited by his daughter Yulia when the attack happened on 4 March.
The pair became ill in the centre of Salisbury after visiting The Mill pub and Zizzi restaurant.
The incident sparked an escalating diplomatic crisis between Russia and the West, with more than 20 countries expelling Russian envoys in solidarity with the UK.
On Thursday, Russia's ambassador to the UN, Vasily Nebenzia, told the UN Security Council that Britain was "playing with fire" and had invented a "fake story".
Mr Nebenzia said Britain's main goal had been "to discredit and even delegitimise" Russia and accused the government of waging a "propaganda war".