The warrant was issued under the concept of universal jurisdiction, which empowers judges to issue warrants for a visitor accused of commiting war crimes anywhere in the world.
'Duty to prosecute'
Pro-Palestinian activists have sought to use the concept to press charges against Israelis involved in military operations in the Palestinian territories, particularly since Israel's offensive on Gaza last year, which killed about 1,400 Palestinians.
"There's no reason why Israel should be singled out for special treatment. If they're accused of war crimes, we have a duty - and legislation - to prosecute"
Inayat Bunglawala, Muslim Council of Britain
Gordon Brown, the British prime minister, has voiced determination to change the law, which has strained relations with Israel.
Ayalon, who discussed the matter with Britain's attorney general on Tuesday, said such warrants "would impede normal bilateral ties".
"This legislation is often misused," he said.
"It initially targeted Nazi criminals, but terrorist organisations like Hamas are today using it to take democracies hostage.
"We have to put an end to this absurdity, which is harming the excellent bilateral relations between Israel and Britain."
But pro-Palestinian groups have condemned moves to change the law, saying Britain has a duty to prosecute those accused of war crimes.
"There's no reason why Israel should be singled out for special treatment. If they're accused of war crimes, we have a duty - and legislation - to prosecute," Inayat Bunglawala, spokesman for the Muslim Council of Britain, told The Associated Press news agency.
The threat of arrest has also forced several former security officials to call off trips to London, including a former general who remained holed up on an airplane at Heathrow Airport in order to avoid arrest.
Last year, Ehud Barak, Israel's defence minister, fended off an arrest attempt by successfully arguing he had diplomatic immunity.