Ms May pointed the finger firmly at Russian President Vladimir Putin overnight as she outlined retaliatory measures in Parliament.
Russia denies any involvement in the attack on ex-spy Sergei Skripal and his daughter Yulia, who have been in a critical condition in hospital since they were found unconscious on March 4 on a bench in the southern English city of Salisbury.
Ms May announced the potential freezing of Russian state assets that pose a security threat, new laws to counter hostile state activity and said British ministers and royals would not attend the football World Cup in Russia later this year.
She had given Moscow until midnight on Tuesday to explain how the Soviet-made Novichok nerve agent came to be deployed on the streets of Salisbury, saying either the Russian state was responsible or had lost control of a stock of the substance.
'Their response demonstrated complete disdain for the gravity of these events,' Ms May said in her statement to Parliament.
'They have treated the use of a military-grade nerve agent in Europe with sarcasm, contempt and defiance.'
The only possible conclusion was that the Russian state was behind the attempted murder of the Skripals and the harm that befell Nick Bailey, a police officer who is in a serious condition after being exposed to the nerve agent, Ms May said.
'This represents an unlawful use of force by the Russian state against the United Kingdom,' she said.
The Russian Foreign Ministry said Moscow would swiftly retaliate against the British measures which had been undertaken for 'short-sighted political ends'.
'The British Government has made a choice in favour of confrontation with Russia,' it said.
The two governments blamed each other for the crisis.
'Many of us looked at a post-Soviet Russia with hope,' Ms May said.
'We wanted a better relationship and it is tragic that President Putin has chosen to act in this way.'
Russia's deputy chairman of the international affairs committee of Russia's Upper House of Parliament, Vladimir Dzhabarov, said he did not rule out Moscow could expel more than 23 British diplomats from Russia, RIA news agency said.
Russia's ambassador in London, Alexander Yakovenko, said Britain's actions were 'absolutely unacceptable' and 'a provocation'.
Some Russia experts cast doubt over whether Ms May's actions would have any impact.
'This is certainly not a strong response from Britain — it is a mild response,' said Mathieu Boulegue, a Russia expert at Chatham House think-tank in London.
'It will not deter Russia because Britain is showing too little steel.'
'Undeclared intelligence officers' given one week to leave
Ms May said the 23 diplomats, identified as 'undeclared intelligence officers', had one week to leave, and Russian intelligence capabilities in Britain would be damaged for years.
Ms May also said Britain would revoke an invitation to Russian Foreign Minister Sergei Lavrov to visit and suspend planned high-level bilateral contacts between London and Moscow.
The Foreign Ministry in Moscow said Mr Lavrov had not accepted the invitation to visit Britain anyway.
Unlike when the United States and European Union imposed sanctions on Russia in response to its annexation of Crimea, Ms May did not name Russian individuals or companies that would be specifically targeted by sanctions.
'We will freeze Russian state assets wherever we have the evidence that they may be used to threaten the life or property of UK nationals or residents,' she said.
She said checks on private flights, customs and freight would be stepped up to better track those travelling to Britain who could represent a security threat.
She also threatened action against those she described as 'serious criminals and corrupt elites', adding: 'There is no place for these people, or their money, in our country.'
Skripal betrayed dozens of Russian agents to Britain before being arrested in Moscow and later jailed in 2006.
He was freed under a spy swap deal in 2010 and took refuge in Britain.
The attack on him was likened in Britain to the killing of ex-KGB agent Alexander Litvinenko, a critic of Mr Putin, who died in London in 2006 after drinking green tea laced with radioactive polonium 210.