The beginning of regular prayers along The Kotel instead of on Har HaBayit (the Temple Mount) apparently starts 360 CE (Byzantium)

There were times like 9 B’Av where we ‘paid’ (read bribed) the Byzantines to let us pray on Har HaBayit.

Between 700 – 1260 prayer was along The Kotel in various locations but primarily inside Warren’s Gate and Mul Kodesh Kedoshim.

The area that is today known as Robinson’s Arch had a cemetery and was also used for prayer most probably during this same time period.  This is where the engravings on the wall under Robinson’s Arch are from.

From 1320 – 1338 the Mamaluks began expanding the Old City by building along / attached to what most people call the Kotel.

Up until 1546/7 there was very limited prayer by the Jews along the Kotel because access was so restricted.  In this year there was a large earthquake in Jerusalem and a number of the Mamaluk building attached to The Kotel crumbled.  In particular in the section that has become know as the Kotel; the main prayer area used today.