Six children are identified by a UNESCO research initiative into child development. The children have extraordinary powers of intellect and are all able to complete a difficult brick puzzle within the same amount of time.
British psychologist Tom Lewellin (Hendry) and geneticist David Neville (Badel) show an interest in Paul, a boy born in London, whose mother Diana (Allen) clearly hates him and claims never to have been touched by a man. This is put down to hysteria, it is implied she has 'loose' morals, but after a while, the two men realize that all six children were born without a father and are capable of telepathy.
The six children from various countries China, Russia, India, Nigeria, the USA and the UK who share this advanced intelligence are gathered in London and housed for collective study.
After international and Cold War tensions lead world governments to ask for their return to their respective embassies, the children murder their government's representatives, escape and take over an abandoned church in Southwark, London. They intermittently take control of the actions of Paul's aunt (Ferris) to help them survive in the derelict church while the military debates whether or not to destroy them. The children have demonstrated the capacity for telekinesis, causing the deaths of several government officials and soldiers.
Lewellin urges the government to give the children a last chance. He and a few scientists observe the difference between an ordinary human blood cell and the body cells of one of the children, Rashid, who has apparently been killed. After a short while investigating the cells, a scientist postulates that they may be human cells but more advanced by a million years.
When authorities try to take control of them, the children are compelled to protect themselves. The situation escalates into a final showdown between armed forces and the children. Rashid emerges from the church alive, but the church is destroyed and the children are killed.