The Independent understands the ground is already being prepared for economic measures such as asset freezes and seizures, alongside visa bans against Russian individuals.
Ms May is also understood to be considering expelling diplomats and pushing for joint international action with allies.
The Prime Minister is set to meet her National Security Council on Wednesday to finalise her approach which is then likely be announced to the House of Commons in the afternoon.
Action came a step closer after the Russian Foreign Minister said his country would not cooperate with the British investigation into the poisoning of ex-spy Sergei Skripal and his daughter Yulia in Salisbury on 4 March.
But Britain’s allies gave early support to Ms May’s push, with German Chancellor Angela Merkel calling for unified action and US President Donald Trump saying there must be “consequences” for those responsible.
It came during another dramatic day on which:
On Monday Ms May delivered an ultimatum to Russia, that it would have to explain how Novichok, a Russian-made nerve agent came to be used in Salisbury.
She warned of “extensive measures” if a full account was not given by midnight on Tuesday, something Foreign Minister Sergei Lavrov declined to do without being handed a sample of the nerve agent identified by the British investigation.
A Government minister told The Independent: “What happens will be an economic war, these will be economic measures.
Russia’s economy is only half that of the UK, a lot of it concentrated in a few people’s hands. Well, we’ll do our bit to make smaller if they want to carry on like this
“Russia’s economy is only half that of the UK, a lot of it concentrated in a few people’s hands. Well, we’ll do our bit to make it smaller if they want to carry on like this.
“That doesn’t give us any pleasure at all, but we need the nations of Europe to behave within the rule of law and not like gangsters. The message has to economic, political and diplomatic.”
A key option open to the Government are powers under the Criminal Finances Act which could see Russian owned assets and property – worth hundreds of millions of pounds in London – thrust under the spotlight.
If individuals who have ties to Mr Putin or are linked to the Salisbury attack cannot show that legitimate means have been used to purchase assets, then they could be seized, as could banked money which is of a suspicious origin.
After former Russian agent Alexander Litvinenko was killed with radioactive poison in 2006, the UK also expelled diplomats, imposed visa restrictions and froze assets of two suspects, but Ms May has indicated she wants to go further this time.
The minister told The Independent the total package of measures being pursued would be “greater than the sum of its parts”.
They went on: “The words that the Prime Minister used were that this constituted an ‘unlawful use of force’, which is important because it does justify proportionate retaliatory action.
“Her main pitch is that we are a country that respects international law and we are going to demonstrate by our adherence to that how much better we are than the gangsterism and lawlessness that characterised this incident.
“So when measures are announced, the total will be greater than the sum of its parts, when you take the overall package of measures announced, they will have force.”
The Government also hopes that the contrast between the UK’s law-based approach and that of Russia’s, will give it credit in international forums like the UN and Nato, and with EU partners.
While ministers know Russia can use its Security Council veto to block a joint-call for sanctions at the UN, diplomats may still push the issue to make a show of isolating Moscow.
One Government insider pointed towards the case of Yvonne Fletcher, the policewoman who was shot from the Libyan embassy in London in 1984, leading to sanctions against Tripoli.
The Independent reported yesterday that ministers had already discussed expelling Russian diplomats from the UK.
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In a diplomatic show of strength ahead of Wednesday, when the international community will watch to see whether she lives up to her threat of “extensive measures”, Ms May held talks with world leaders.
A Downing Street spokesman confirmed the Prime Minister had talked with Chancellor Merkel on Tuesday afternoon to update her on the on-going investigation.
He said: “They discussed the pattern of aggressive Russian behaviour and agreed it would be important to act in unison with allies to counter it.
“Chancellor Merkel condemned the attack and said she stood in full solidarity with the UK.
“They agreed that the international community should coordinate closely as the investigation developed and in the wake of Russia’s response.”
On Monday Mr Tillerson strongly backed Ms May’ approach and the British government’s assessment about it being “highly likely” that Russia ordered the attack in Salisbury.
But at the regular White House press briefing the President’s press secretary, Sarah Sanders, refused repeatedly to assign blame to Russia.
Mr Trump then also appeared unwilling to do so as he spoke to reporters on Tuesday, but the Number 10 spokesman said that in a call Mr Trump had told Ms May the US is “with the UK all the way”.
Readouts of the call from both sides underlined that the two leaders agree that “the Russian government must provide unambiguous answers as to how this nerve agent came to be used”.
The White House readout went further adding that the pair also agreed “the need for consequences for those who use these heinous weapons”.