If he does, or doesn't, the line dies with him. It would have to continue through his female maternal cousins. Mitochondrial DNA is completely inherited from the mother. This is because it's not in the nucleus of the cell, where all that sexual stuff goes on, but rather out in the mitochondria, which are present in the ovum before it's ever fertilized, and to which the sperm does not contribute anything.
They only tested a handful of people living in country. Cheddar man may have thousands of relatives living elsewhere.