Russian intelligence agencies targeted poison victim Yulia Skripal's email account as early as 2013, the UK's national security adviser has said.
In a letter to Nato, Sir Mark Sedwill also said Russia trained "special units" to use nerve agents, including applying them to door handles.
Police said a nerve agent was found on Yulia's father Sergei Skripal's front door in Salisbury.
The Russian government has denied any involvement in the 4 March attack.
The UK says Ms Skripal, 33, and her 66-year-old father, who were found slumped on a park bench in the city on 4 March, were exposed to a nerve agent belonging to the Novichok group.
This analysis has been backed by the international chemical weapons watchdog.
Mr Skripal remains at Salisbury District Hospital, while his daughter was discharged on Monday.
Sir Mark's letter to Nato Secretary General Jens Stoltenberg is the first time the UK government has claimed to have specific information that the Russians were interested in the Skripal family.
"We have information indicating Russian intelligence service interest in the Skripals dating back at least as far as 2013," he said.
"Email accounts belonging to Yulia Skripal were targeted by GRU cyber specialists," he said, referring to Russia's foreign military intelligence agency.
The letter accuses Russia of testing assassination methods with chemical weapons, including using nerve agents smeared on to door handles.
Police say traces of a Novichok nerve agent have been found at sites across Salisbury at low concentrations following the attack - with the highest concentration found on the door handle of Mr Skripal's front door.
No 10 has released a letter from National Security Advisor Mark Sedwill to NATO Secretary-General. It spells out more details of intelligence pointing to Russia in the Salisbury case. Includes suggestion that Russia was specifically looking at putting nerve agents on door handles pic.twitter.com/hd7Yu4z6y8— Daniel Sandford (@BBCDanielS) April 13, 2018
But the details contained in the letter do not identify the exact culprits behind the poison attack.
Sir Mark said it was "highly likely" people such as Mr Skripal, who was exchanged in a spy swap in 2010 after being convicted of passing information to the UK, may be regarded as "legitimate targets" for "state-sponsored assassination" by Russia.
He said the UK government continued "to judge that only Russia has the technical means, operational experience and motive for the attack on the Skripals and that it is highly likely that the Russian state was responsible".
"There is no plausible alternative explanation," he added.
The letter also claims President Vladimir Putin was closely involved in the Russian chemical weapons programme in the mid-2000s, and that it was "highly unlikely" any former Soviet republic other than Russia pursued chemical weapons after independence.
The Russian embassy has published an 8,000-word report on the Skripal case, including a timeline and details of the British response.
The report accuses the British government of isolating the Skripals, concealing evidence and preventing an independent investigation.
It also says the UK is using "the same script, but in fast forward mode" as it did on the case of Alexander Litvinenko - the former Russian agent poisoned in London in 2006.
Meanwhile, Metropolitan Police Commissioner Cressida Dick has said around 250 detectives were working on the Salisbury investigation.
She said they would do everything to establish the facts and "if at all possible" bring those responsible to justice.