Was Perham Down used as a base for foreign troops in the First World War - I am interested especially in the period 1917-1918 and the possibility of South African units being there
After the Gallipoli Campaign, the Australian Imperial Forces joined the allies on the Western Front, and in support of the Divisions at the front, Training Battalions were formed in this country. No. 1 Training Group was established at Perham Down, and it provided accommodation for 160 officers and 4878 NCOs and other ranks.
Also, there were four Command Depots established to receive men discharged from hospital - one for each category of fitness. One such depot was established at Perham Down, for soldiers deemed fit enough to rejoin their units in France.
So the short answer is that it was occupied by Australians, not South Africans. For further enlightenment you could post a question to the South African Military History Society, at firstname.lastname@example.org, or inquire of the Imperial War Museum's reading room, at email@example.com. The latter holds Official Histories of the various armed forces in the Great War, and much else besides. Failing these approaches your only recourse would be either to the UK National Archives - check www.nationalarchives.gov.uk, or to the South African National Archives - check www.nationalarchives.gov.za, or the South African Military History Society's guide to contacts for military history at the South African National Archives at www.samilitaryhistory.org/mussocco.html.
However, having discussed your inquiry in more detail, and learning that your inquiry relates to an individual from South Africa whose main service record for the period of the Great War hostilities you already have from the National Archives, I am afraid that your only sensible recourse is further archival research. But without any information on the regiment or corps in which your grandfather served after the Great War, we cannot even provide pointers as to where you should begin looking.
James, N.D.G.: Plain soldiering: a history of the Armed Forces on Salisbury Plain (Hobnob Press, 1987), pp. 63, 80, 81.