Police are appealing for information on Alexander Petrov (left) and Ruslan Boshirov
Two Russian nationals have been named as suspects in the attempted murder of former Russian spy Sergei Skripal and his daughter Yulia.
The men, using the names Alexander Petrov and Ruslan Boshirov, are thought to be officers from Russia's military intelligence service, the PM said.
Scotland Yard and the CPS say there is enough evidence to charge the men.
Mr Skripal, 66, and his daughter Yulia, 33, were poisoned with the nerve agent Novichok in March.
Det Sgt Nick Bailey also fell ill after responding to the incident in Salisbury.
Police are linking the attack to a separate poisoning on 30 June, when Dawn Sturgess and Charlie Rowley became unwell at a house in Amesbury, about eight miles from Salisbury.
Ms Sturgess died in hospital on 9 July. Mr Rowley was discharged from hospital on 20 July.
Speaking in the Commons, Prime Minister Theresa May said the government had concluded, from intelligence provided by UK agencies, that the men were part of the GRU intelligence service.
The poisoning was "not a rogue operation" and was "almost certainly" approved at a senior level of the Russian state, she said.
"On the basis of what we have learnt in the Salisbury investigation and what we know about this organization more broadly, we must now step up our collective efforts specifically against the GRU," she said.
Mrs May promised "the full range of tools from across our national security apparatus" would be used to "counter the threat" caused by Russia.
She condemned the "sickening and despicable attack" which "left four people fighting for their lives and one innocent woman dead".
Labour leader Jeremy Corbyn said the use of military-grade nerve agent on the streets of Britain was an "outrage and beyond reckless".
Yulia and Sergei Skripal fell ill after Mr Skripal's front door was sprayed with Novichok
The two suspects, believed to have been using aliases, travelled on Russian passports and are thought to be about 40.
The CPS is not applying to Russia for the extradition of the two men, as Russia does not extradite its own nationals.
But a European Arrest Warrant has been obtained in case they travel to the EU.
In response, the Russian foreign ministry has said the names and photographs of the men "do not mean anything to Moscow".
Sue Hemming, CPS director of legal services, said there was enough evidence "to provide a realistic prospect of conviction" and that it was "clearly in the public interest to charge Alexander Petrov and Ruslan Boshirov".
The offences include conspiracy to murder Sergei Skripal; the attempted murder of Sergei Skripal, Yulia Skripal and Nick Bailey; the use and possession of Novichok contrary to the Chemical Weapons Act; and causing grievous bodily harm with intent to Yulia Skripal and Nick Bailey.
Scotland Yard's Assistant Commissioner Neil Basu, the head of UK counter-terrorism policing, said on Wednesday that Det Sgt Bailey "continues to make good progress but remains off work".
What happens now?
Analysis by BBC News diplomatic correspondent Jonathan Marcus
The decision to name two Russian individuals as suspects in the Skripal case is a significant developmentraising the level of evidence on which the British government's charges are based and potentially giving added weight to calls for additional international sanctions against Moscow.
The United States, along with a swathe of Britain's allies, expelled a significant number of Russian diplomats (many thought to be intelligence agents) in the wake of the initial evidence that a Russian military grade nerve agent had been used in the Salisbury attack.
Since then, the United States administration has brought in some additional measures mandated by Congressand more are likely to be on the wayeven though President Trump himself has not shown great enthusiasm for further pressure on Russia.
Britain will be hoping that other countries may now show more enthusiasm for stepped-up sanctions.
The Metropolitan Police said the two men arrived at Gatwick Airport from Moscow on 2 March and stayed at the City Stay Hotel in Bow Road, east London.
On 4 March they travelled to Salisburyhaving also visited for reconnaissance the previous day -where Mr Skripal's front door was contaminated with Novichok.
Officers believe a modified perfume bottle was used to spray the door.
While traces of Novichok were found in the London hotel room, there is no risk to other guests who were staying at the hotel at the time, police said.
They now want to hear from anyone who was a guest there from 4 March to 4 May.
London Mayor Sadiq Khan said he had been assured by Transport for London and police that there was no risk to public health in London.
Police said Ms Sturgess and Mr Rowley were later exposed to Novichok after handling a contaminated container, labelled as Nina Ricci Premier Jour perfume.
Mr Rowley has told police he found the box containing the small bottle and an applicatorall later found to be counterfeitin a charity bin.
He tried to put the two parts together and got some of the contents on himself. His partner Ms Sturgess applied some of the contents to her wrists and became unwell.
The bottle, with a modified nozzle, had contained a "significant amount" of Novichok, Scotland Yard said.
Mr Basu said: "We don't yet know where the suspects disposed of the Novichok they used to attack the door, where Dawn and Charlie got the bottle that poisoned them, or if it is the same bottle used in both poisonings."
But he also stated that "the manner in which the bottle and packaging has been adapted makes it a perfect cover for smuggling the weapon into the country, and a perfect delivery method for the attack against the Skripal's front door".
Mr Basu confirmed that the two cases were related, saying: "We have now linked the attack on the Skripals and the events in Amesbury which affected Dawn Sturgess and Charlie Rowley.
"It now forms one investigation. We do not believe Dawn and Charlie were deliberately targeted, but became victims as a result of the recklessness in which such a toxic nerve agent was disposed of."
The reaction from Russia
BBC Monitoring
Political talk shows on the main Kremlin-controlled national channels interrupted their broadcasts to mention the news.
As before in Russian media reaction to what they call the "Skripal affair", sarcasm and disbelief at the British government's actions were the domit themes.
"We are expecting new sanctions, of coursewith pleasure," a prominent talk show host said live on air on channel Rossiya 1.
Over on Channel One, a host stated that even though it had taken Britain "roughly half a year" to name the suspects, sanctions had been imposed on Russia long before this.
"Is this how this just world, where everybody loves each other, looks like?" he asked a guest advocating that the Kremlin soften its policy towards the West.