In 'Notes and Queries for Worcestershire' (1856) John Noake explains on p204 that:
At Dudley there is a tradition that many years ago a giant lived in Dudley castle, as did also one in the castle of Birmingham. The Birmingham giant had done suit and service to the Dudley giant for many years, but growing fat he began to kick, and refused to serve the Dudley giant longer. A furious dispute thereupon broke out; the Dudley giant in his rage threw a large stone all the way from Dudley at the Birmingham giant and demolished his castle and killed him. Some of his surviving followers erected a stone in the lane as a memento of his prowess and rage and called it the War Stone, whence the name Warstone Lane.
Online at Google Books.
The stone has also been known as the Whorestone or Hoarstone.
It can be found just inside the cemetery in Warstone Lane.