Using documents obtained under freedom of information laws, the BBC says that Britain deliberately misled the International Atomic Energy Agency. Mike Michaels, Britain's representative to the IAEA, reportedly played a critical part in assisting Israel.
Michaels knew that supplying Israel with a small quantity of plutonium would allow the country to develop nuclear weapons much sooner.
In the heavy water sale, Britain had bought a surplus from Norway. The sale to Israel was done through an intermediate company, the BBC said.
Tony Benn, who served as technology minister under Wilson, said he was unaware of the export of nuclear materials to Israel at the time.
"I'm not only surprised, I'm shocked," he said.