The judge ruled that the Defense Minister enjoys diplomatic immunity because he is Britain on an official visit.
Earlier in the day, the court said it was postponing the hearing on the petition.
Barak, chairman of the Labor party, attended a British Labor party conference on Tuesday and met with Prime Minister Gordon Brown.
His appearance at the conference rubbed salt in the wounds of pro-Arab supporters. "As a high contracting party to the Geneva Convention, the British government should be arresting Barak for war crimes, not treating him to dinner," said Palestine Solidarity Campaign official Becky Hunter.
Acting on the advice of Israeli legal authorities, Barak decided to remain in Britain despite the petition for a decision ordering his arrests. He is to meet with Foreign Minister David Miliband on Wednesday.
The petition requested that Britain take the Defense Minister into custody under a British law that gives the country's courts jurisdiction in cases of war crimes.
The court case followed last week's United Nations Human Rights Commission report issued by retired South African Judge Richard Goldstone, who accused Israel of war crimes in the Cast Lead campaign. Goldstone also concluded that Hamas may be guilty of war crimes.
Previous threats to arrest Israeli political leaders and military officers have been taken seriously. Senior IDF officer Doron Almog remained on a plane after landing in Britain after learning that he might be arrested for alleged crimes.