The prime minister is "incapable" and is in a "weak position" in his talks with Brussels, according to the former UKIP leader, who compared the EU to Glenn Close's deranged stalker at Fatal Attraction.
Mr. Farage claimed to have seen the minutes of an EU meeting that "despised" Mrs. Mayor's plans on the tax.
The document shows that the EU negotiating team of Michel Barnier wants to repress UK business by preventing Britain from diverging with Brussels in taxes, according to Mr Farage.
Writing in the Daily Telegraph, Mr. Farage said: "It is clear that the EU wants to achieve two things: First, it wants to limit the opportunities for the United Kingdom to be competitive and prosperous.
"Second, he wants to sow the division between the United Kingdom and its overseas territories."
He added: "So far, Theresa May has proven herself unable to escape this monster of intimidation.
"I wonder what she will need for her to understand the severity of the punishment that the EU boys want to inflict on us.
"Theresa May is in a weak position due to the submissive stance she has always shown in dealing with Brussels, it is time for Ms. May to show something of value and to defend Britain.
"I shudder to think what the implications will be if she does not take the initiative and make sure that the EU's tentacles stay away from the fiscal affairs of this country forever."
The minutes of the meeting describe Mrs. May Checkers' plans as "illusions," Farage said.
The European Commission intends to pressure Ms. May to make a commitment that the UK and its overseas territories abide by the EU Code of Conduct for Corporate Tax after Brexit, he added.
However, such a move could cause the British overseas territories to press for the independence of the United Kingdom while they seek to maintain their autonomy over their tax systems, Farage said.
He said: "This is another example of the imposition of the EU, or the quest to impose, in Britain when it has absolutely nothing to do to do it.
"Like the creepy stalker in Fatal Attraction who refuses to accept that the relationship is over, he keeps coming back with escalating demands and threats."