The Damned

Simon Wells, a middle-aged tourist, is on a boating holiday off the southern coast of England. He has recently divorced, and left his career as an insurance executive. In Weymouth, he meets 20-year-old Joan, who lures him into a brutal mugging at the hands of her brother, King, and his motorbike gang. The next day Joan defies her overprotective brother and joins Simon on his boat.
Simon is willing to forgive the prior incident, and Joan implies that the beating was inevitable after Simon attempted to pick up Joan in a bar. She describes the abuse she suffers from King whenever men show interest in her. Simon urges her to run away with him, but she insists upon returning to shore. Their time on the water is observed by a member of King's gang.
That night, Joan and Simon meet at a cliff-top house where they have sex. The house is surrounded by King's gang, but the couple escape and reach the relative safety of a nearby military base. They are taken to meet the base commander, a scientist named Bernard. He refuses to discuss his work and deflects their questions with vague threats. Joan and Simon are free to leave.
The couple descend the cliff to the beach, pursued by King. They find a network of caves leading to an underground bunker attached to the military base. Within the caves live nine children, all aged 11, whose skin is cold to the touch. They appear healthy, well-dressed, and intelligent, but know little about the outside world. Their home is under continuous video surveillance. They are educated via closed circuit television by Bernard, who deflects their questions about their purpose and their isolation with promises that they will learn the answers someday. The children are regularly visited by men in radiation protection suits.
Although Bernard is forced to keep the children under constant watch, he allows them one chamber in the caves without cameras. The children are unaware that their "secret hideout" is known to their captors, and they keep there mementos of people that they believe are their parents. The children host Joan, Simon and King in this "secret" room and smuggle food to them. Joan and Simon commit to rescuing the children, and they pressure King into helping them. The three visitors soon feel unwell.
Bernard urges the children to give up their new friends, and reveals his knowledge of their secret place. The children refuse, and destroy the surveillance cameras. Bernard sends men in radiation suits, but King and Simon overpower them. Simon uses one of their Geiger counters, and discovers that the children are radioactive. The intruders lead the children out of the caves, but they are ambushed by more men in radiation suits and most of the children are taken back to the bunker.
King grabs one of the boys and escapes in a stolen car. He is overcome by radiation sickness and orders the boy out of the car. The boy is immediately recaptured. King is pursued by a helicopter, loses control of the car and is killed.
Joan and Simon escape by boat, but they are also overcome by sickness. A helicopter hovers above as their boat drifts off course; the pilot has orders to destroy it once the occupants are confirmed dead.
Bernard confides in his mistress Freya that he regrets the children now know they are prisoners. They were born radioactive, engineered to be resistant to nuclear fallout in order to survive the "inevitable" nuclear war to come. When Freya rejects him and his plan, he kills her.
The final scene depicts holiday-goers enjoying the beach, unable to hear the desperate cries of the imprisoned children nearby.

Question: What kind of sickness is King overcome by?
Answer: radiation sickness