There are a couple of missions a player can recieve via radio transmission. A signal will announce you have recieved a message, after which a message at the bottom of the screen flashes that to accept one should press (standard key) enter. This will play the message.
A radio message works exactly the same as a quest npc once the conversation is started, one can flip through the pages of the message and accept or cancel.
According to lore Hellgate: London Exodus, just after the invasion communication with London broke down rapidly. At first there have been images of demons and humans fighting, but less and less new footage made it out of London. Normal communications via radio were interrupted soon after that footage. It was speculated that some demons took out sattelites, though it's probably meant that they took out the satalite uplinks. When main character Simon wonders about the lack of information, he says the Templar have short-wave radio's, which in contrast to other radio, apparently should be immune to the static interferance caused by either the Hellgate or The Burn