Becks, 35, acted after her claims he had a threesome with her and another vice girl were first published in the US.
He has given his worldwide team of lawyers a blank cheque to clear his name.
And they will DEMAND a front-cover apology from the US magazine that published the vice girl's sordid claims that Becks paid for sex with her and another prostitute.
Irma scurried into hiding as dad-of-three Becks and his wife Victoria put on a united front in Los Angeles.
A pal of the LA Galaxy playmaker said: "David is prepared to scour the Earth for this woman, who seems to think she could make up a complete fantasy that is extremely hurtful to him and and his family.
"She has treated his wife and children with such disregard he is not prepared to let this one go.
"He wants everyone held accountable. The magazine, the publishers and the hooker."
Bosnian-born Irma, who was raised in Britain, claimed New York's Le Parker Meridien hotel was the venue for the threesome in 2007.
But the pal said: "David can prove he wasn't there. She cannot prove he was."
Former England captain Becks has branded the allegations "a series of malicious lies".
Posh Spice Victoria, 36, yesterday told relatives she is standing firmly by her husband - and is "bloody furious" the story will upset the pair's children Brooklyn, 11, Romeo, seven, and Cruz, five.
A source said: "She knows these allegations are a complete falsehood and they will tackle this problem head on, together, as a family.
"Let's not pretend Victoria wasn't upset, because she was.
"You don't want your name plastered all over the media in that context even if it is complete lies. But she and David won't let it beat them. They are strong and united."
Irma claimed Beckham paid her £3,200 to have sex in the Manhattan hotel while he was there for a Galaxy game against New York Red Bulls.
In her story, splashed across the cover of In Touch Weekly magazine, she alleged he paid another £1,500 for a second vice girl to join in. Beckham's legal team believe there are a string of inconsistencies in her lurid account.
Last night the player was drawing up a battle plan with top US trial lawyer Bert Deixler.
Gerrard Tyrrell, senior partner at London media lawyers Harbottle & Lewis, is on board to look after Beckham's UK interests.
And a team of German legal experts are involved as the magazine is published by Hamburg-based media group Bauer, which operates in 15 countries including Britain.
The lawyers are seeking an undertaking from In Touch Weekly that it will never repeat Irma's story in print or online.
US media law expert Sandy Baron said: "David Beckham would be entitled to punitive damages that potentially could run into the millions, particularly if he can prove the allegations were malicious or published with total disregard for the truth.
"The figure suggested of £5million is certainly possible."
Posh and Becks made a point of acting normally after the story emerged on Wednesday. He trained with his Galaxy team-mates and she headed to a gym.
Later they were seen together in a black Range Rover. It is believed they were on their way home from dinner in Los Angeles.
Beckham went training again yesterday as he continued to fight to regain full fitness following the Achilles injury that ruled him out of the World Cup.
Irma worked for notorious ex-New York madam Kristin Davis, who had 2,000 punters on her books.
Several A-list celebrities are now worried other hookers may tell stories to magazines, whatever the truth of the matter, because of the inevitable aggravation it would cause.
A source said: "With this girl coming forward to make these claims, even though they are a pack of lies, there is a concern others will follow her lead and try the same thing."
Kristin is now running for Governor of New York on a ticket of decriminalising prostitution.