These are the Damned
(1963)

Simon, an American traveling in England, meets Joan, a young British lady. Joan's brother King (Oliver Reed) is leader of a vicious gang of thugs.  King does not want his sister with Joan.  Simon and Joan are pursued by the gang, and as they flee end up in a secret military base.  On the base, they discover a group of children kept in isolation.  The children are under the supervision of a man named Bernard.  They are fed by men in radiation suits.

They discover the kids are radioactive. Still,  Joan, Simon and King decide to try and help the kids escape.  The men in radiation suits capture the kids. Joan and Simon are allowed to leave in his boat, as the men know they will die of radiation sickness from their contact with the children.  

Bernard reveals that he is convinced that nuclear war is coming.  Humans will be unable to survive on a radioactive planet.  He has engineered these radioactive children as the future of humanity, to populate the earth after the nuclear war.

Thanks Joseph C!