This tomb in a quiet garden is venerated by many as the tomb of Christ: it conforms to the expectations of simple piety and it is outside the walled city. It is much easier to pray here than in the Holy Sepulchre. Unfortunately there is no possibility that it is in fact the place where Christ was buried.
The first visitor to popularize this site as Golgotha was General Charles Gordon in 1883: he thought he recognized the shape of a skull in the hill behind the tomb. The excavation of the nearby Church of St Stephen, and in particular the discovery of the tombstone of the deacon Nonnus which mentioned the Holy Sepulchre, quickly convinced Protestants desirous of having a Holy Place of their very own that this was the place where the Byzantines located Calvary and the Tomb. Despite the protestations of those best qualified to judge, the Anglican Church committed itself to the identification, and what had been known scornfully as ‘Gordon’s Tomb’ suddenly became the ‘Garden Tomb’. Sanity eventually prevailed, and the Anglican Church withdrew its former support, but in Jerusalem the prudence of reason has little chance against the certitude of piety.
Source: The Holy Land by Jerome Murphy- O’Connor