"We are dismantling the Russian espionage network in our country and we will not allow it to be rebuilt," she said.
"Following the incident in Salisbury we have of course taken further measures.
"We are urgently developing proposals for new legislative powers to harden our defences against all forms of Hostile State Activity.
"This will include the addition of a targeted power to detain those suspected of such activity at the UK border; and considering whether there is a need for new counter-espionage powers to clamp down on the full spectrum of hostile activities of foreign agents in our country.
"We are making full use of existing powers to enhance our efforts to monitor and track the intentions of those travelling to the UK who could be engaged in activity that threatens the security of the UK and our allies.
"This includes increasing checks on private flights, customs and freight and freezing Russian state assets wherever we have the evidence that they may be used to threaten the life or property of UK nationals or residents.
"We are also cracking down on illicit and corrupt finance, bringing all the capabilities of UK law enforcement to bear against serious criminals and corrupt elites – neither of whom have any place in our country.
"We have given our law enforcement agencies new powers in the Criminal Finance Act and we will table an amendment to the Sanctions Bill to ensure that the UK cannot be a home for those who trade illicit finance or commit human rights abuses," the PM said in a statement.
As reported, Russian ex-spy Sergei Skripal, 66, and daughter Yulia Skripal, 33, remain critically ill in hospital, after they were found unconscious on a bench in the Wiltshire city on March 4. The UK government says they were poisoned with a nerve agent of a type developed by Russia called Novichok and PM Theresa May said she believed Moscow was "culpable."
UK expelled 23 Russian diplomats as part of a "full and robust" response – prompting Russia's Foreign Minister Sergei Lavrov to say it will "certainly" expel British diplomats in response.
On March 16, Nato Secretary General Jens Stoltenberg said the alliance had "no reason to doubt the findings and assessments by the British government" which suggested Russian responsibility. He said the "UK is not alone" and Nato allies gave "strong political support" to Britain, following a joint statement from the US, France and Germany backing Mrs May's government and a pledge of support from Australia.
British Foreign Minister Boris Johnson said that the U.K.'s government believes that it was likely Putin's decision to direct the use of a nerve agent on the streets of the U.K.
U.S. President Donald Trump on Monday ordered the expulsion of 60 Russians from the United States on Monday, including 12 people identified as Russian intelligence officers who have been stationed at the United Nations in New York.