I saw it in the late 80s-early 90s at an art house cinema. (God, I miss those.) It takes place in the plagues of yore in a coal-mining community in England. For some reason the desperate townsfolk thought they could get to a safe, faraway land if they went as far down the mine as possible. I guess the shaft tapped into a deep cavern.
Anyway, a young boy was chosen to lead the way. Eventually, they eventually do find their way to another land, New Zealand. And also to another century, the 20th. I don’t remember much about their time there but I was much more engaged than similar Twilight-Zony fare. Finally they climb back to their own village and time. The plague had subsided and much merriment abounded. Then the boy pulled back his shirt collar to show the growing black mass of the plague. All very fraught with symbolism.
That’s the one! There was another period movie around the same time called The Pathfinder, which also featured a boy leading a group of men, but in Sweden I think. I used to get them confused until I just forgot The Navigator altogether.