To answer the question very directly, when a squaddie's child went missing in Sennelager, Germany many years ago, both the local and military police were involved and there was wide coverage on the German and Forces TV. I don't know about in the UK, we were in Germany. Nothing was found after months and has never been found since, the case occasionally crops up in the UK press. I recall it because we were in the NAAFI that afternoon and the missing girl was the image of our daughter.
But we now live in a different world of communications, an event can hit the media very quickly and be kept there. When the McCann case happened, it was, I believe, on the national news the same evening in the UK, so someone managed to move quickly.