The Islamic Human Rights Commission (IHRC), based in London, is seeking high court permission to bring proceedings against the Civil Aviation Authority, the Foreign and Commonwealth Office and Des Browne, the secretary of state for defence, to prevent them from what it says are crimes against the Geneva Conventions.
A number of US aircraft believed to be carrying military hardware to Israel refuelled in the UK during the Lebanon conflict.
Massoud Shadjareh, chairperson of the IHRC, on Tuesday described the organisation's action as "an attempt to force the relevant public authorities to respect the law as they know parliament has laid down for all UK citizens to respect and follow, but which our government refuses to abide by".
"We hope that the independent court will finally uphold the will of parliament and enforce the law."
Earlier this month, British police arrested seven anti-war activists after three of them boarded a US military transport plane at an airport in Scotland to check if it was carrying weapons to Israel.
Anti-nuclear campaign group Trident Ploughshares said the airport was used by chartered cargo planes to carry US-made bunker-busting bombs to Israel during the war in Lebanon.
A spokesman for the group said that "by colluding with the US supplying Israel with bombs, Britain is colluding in war crimes."
No bombs were found on the plane and it was not known if it was bound for Israel.
Last month, a stopover at Prestwick of US flights carrying missiles to Israel sparked intense criticism in Britain.