Speaking at the Conservative spring forum on Saturday, Theresa May said Britain would never tolerate a threat to the life of its citizens, or others in the country, from the Russian government.
This act of Russian aggression is the very antithesis of the liberal and democratic values that define the United Kingdom, she said.
The pledge comes as 23 British diplomats based in Russia begin packing their bags as they are expelled from the country in retaliation for Russian representatives being told to leave the UK.
It is thought most or all are intelligence officers.
Russia has also shut down the offices of the British Council in Moscow a move the cultural organisation says is profoundly disappointing
It is our view that when political or diplomatic relations become difficult, cultural relations and educational opportunities are vital to maintain ongoing dialogue between people and institutions, a statement said.
Russia has insisted that aggression is on the side of the UK, with the head of the country’s foreign affairs committee calling the moves following the poisoning a decision by the British side without evidence.
The escalating tensions come as Russia is preparing for its general election.
Other moves by the UK in response to the poisoning include legislative powers to defend against hostile state activity and the suspension of high-level contacts between the US and the Russian Federation.
As the fallout from the poisoning unravels in the international arena, British police are continuing their investigation into the poisoning of Mr Skripal and his daughter Yulia.
They have renewed appeals for information about a burgundy BMW belonging to the former spy, which is believed to have been driven around Salisbury on the morning of the poisoning.