The secrets of what lay behind the first nerve agent attack in Europe since the Second World War are likely to be revealed with Sergei and Yulia Skripal expected to speak to investigators in the coming days after making a remarkable recovery.

The former MI6 spy and his daughter may soon be in a position to reveal to investigators the chain and time of events leading up to her poisoning and that of her father in Salisbury a month ago – and who may have carried out it out.

Despite the head of Porton Down, the military research centre, saying there is no known antidote to the military grade novichok, which Theresa May’s government has said was used in the attempted murders, both now appear to be out of danger.

The timing of their interviews will be dependent on advice of the specialist medical staff treating them, but the police and security agencies are optimistic that the answers to what took place are likely to emerge soon.

Salisbury District Hospital, where the pair have been treated since being struck down last month, said Mr Skripal was “responding well to treatment, improving rapidly and no longer in a critical condition”.

Yulia Skripal, who had issued a public statement through the police saying she “woke up a week ago and am glad my strength is growing daily”, will be questioned before her father unless his condition improves dramatically.

Ms Skripal supposedly spoke on the telephone with her cousin Viktoria in Moscow who was due to visit her in hospital. During the call Yulia told Viktoria she may not be given a visa, and yesterday the UK authorities confirmed that the visa application has been refused.

This led to an immediate charge of further cover-up by Russian officials who have already accused the UK of carrying out the attack.

A Home Office spokesman said: “We have refused a visitor visa application from Viktoria Skripal on the grounds that her application did not comply with the immigration rules.”

Sergei Lavrov says the British government could have poisoned the Skripals themselves

Russian state television earlier this week broadcasted a telephone conversation between Viktoria and her cousin, where Yulia allegedly said “everything is fine” and her father was “sleeping”.

Foreign Secretary Boris Johnson said the improvement in the condition of Mr Skripal was “great news” and “testament to the quick work” of the emergency services.

Dr Christine Blanshard, medical director at Salisbury District Hospital, said speculation about when the two could be released from hospital was “just that – speculation”.

The Foreign Office said the pair were “likely to have ongoing medical needs”.

“We are very pleased that both Mr Skripal and his daughter Yulia are improving,” a spokesman said. “This is a tribute to the hardworking and talented NHS staff in Salisbury who have provided outstanding care.

“Let us be clear, this was attempted murder using an illegal chemical weapon that we know Russia possesses.”

The Russian Embassy said it hoped the improvement in the Skripals’ health will “contribute to the investigation of the crime perpetrated against them”.

Skripal attack aftermath – in pictures Show all 15 1 /15 Skripal attack aftermath – in pictures Skripal attack aftermath – in pictures Scene of attack Members of the emergency services in hazard suits fix the tent over the bench where Sergei and Yulia Skripal were found unconscious on a park bench in Salisbury in March 2018. Getty Skripal attack aftermath – in pictures Victim - Sergei Skripal The retired Russian colonel and former double agent for MI6 was in a critical condition in hospital for more than two months after being exposed to novichok in Salisbury. He was given refuge in the UK after being jailed in Moscow for treason. Mr Skripal came to Britain as part of a high-profile “spy swap” in 2010 in which four men were exchanged for ten Russian "sleeper agents" in the US. In this image he is speaking to his lawyer from behind bars in Moscow in 2006. AP Skripal attack aftermath – in pictures Victim - Yulia Skripal Yulia Skripal was struck down by a novichok poison alongside her father Sergei. Facebook Skripal attack aftermath – in pictures Scene of attack A police officer stands guard outside a branch of the Italian chain restaurant Zizzi where the pair dined at before falling ill. It was boarded off whilst investigators worked on the building and later found traces of the chemical weapon within it. AFP/Getty Skripal attack aftermath – in pictures Scene of attack Large areas of central Salisbury were cordoned off by police following the discovery of the Skripals. Traces of nerve agent were also found in The Mill pub. PA Skripal attack aftermath – in pictures Victim - Nick Bailey Detective Sergeant Nick Bailey, rushed to the aid of the Russian ex-spy and his daughter who were targeted with a nerve agent. He was hospitalized after aiding them and didn't leave until three weeks after the attack. Wiltshire Police/Rex Skripal attack aftermath – in pictures Police investigation - Skripal’s home Police believe they were poisoned at home, and detectives found the highest concentration of novichok on the front door of Mr Skripal’s house. Getty Skripal attack aftermath – in pictures Theresa May visits scene of attack Britain's Prime Minister Theresa May spokes with Wiltshire Police's Chief Constable Kier Pritchard near where the Skripal's were found. Britain expelled 23 Russian diplomats over the nerve agent poisoning and suspended high-level contacts, including for the World Cup on March 14. Theresa May told parliament that Russia had failed to respond to her demand for an explanation on how a Soviet-designed chemical, Novichok, was used in Salisbury. AFP/Getty Skripal attack aftermath – in pictures Skripal days before attack Sergei Skripal days before he was exposed to Novichok, that has left him fighting for life. ITV News Skripal attack aftermath – in pictures Police investigation - military involvement British soldiers were deployed soon after the attack to help a counter-terrorism investigation into the nerve agent attack. One of the places they were asked to help out with was Skripal's home and it's surrounding. They were asked to remove a vehicle connected to the agent attack in Salisbury, from a residential street in Gillingham. AFP/Getty Skripal attack aftermath – in pictures Police investigation Personnel in protective coveralls and breathing equipment cover an ambulance with a tarpaulin at the Salisbury District Hospital. AFP/Getty Skripal attack aftermath – in pictures Police investigation The investigation extended to the grave of Sergei Skripal's son Alexander in London Road cemetery. Getty Skripal attack aftermath – in pictures Police investigation The Counter Terrorism Policing Network requested assistance from the military to remove a number of vehicles and objects from Salisbury. EPA Skripal attack aftermath – in pictures Home Secretary visits scene of attack Home Secretary Amber Rudd visited the scene of the nerve agent attack at the Maltings shopping centre on 9 March. Getty Skripal attack aftermath – in pictures Yulia Skripal speaks for the first time Yulia Skripal, speaking for the first time, said she felt lucky to have survived the nerve agent attack in Salisbury which left her fighting for life. Ms Skripal said her life had been “turned upside down” by the assassination attempt. But the Russian national added she hoped to return to her homeland one day, despite the Kremlin being blamed for the attack. Reuters

Dan Kaszeta, a security and chemical defence consultant, said nerve agents are quick acting if they are inhaled, which did not appear to be the case with the Skripals.

“We do not know the narrative of that afternoon in detail, for example Sergei – what did you touch and when did you touch it?”

Now that Ms Skripal in particular is known to be recovering and talking, her insight into what happened will be “extremely important”, Mr Kaszeta added.

The development came as Donald Trump heightened diplomatic tensions further by announcing sanctions against seven Russian oligarchs with ties to Vladimir Putin for “malign activity” around the world.

Meanwhile, Russia is demanding an explanation over the deaths of two guinea pigs and a cat that was found in a distressed state at Mr Skripal’s house.

The Russian Embassy said: “Regarding the dead guinea pigs and the malnourished cat, it is said unofficially that they were taken to the Porton Down facility and incinerated there.

“But it remains unclear if their remains were ever tested for toxic substances, which would constitute useful evidence, and if not why such a decision was made.