The HG series of convoy ran from Gibraltar (HG.7 - 9 from Port Said) to the UK from September 1939 until the advent of Operation Torch in September 1942. During this period, occasional, additional convoys, designated SLG also sailed. The HG series did not restart but was replaced by the MKS series from November 1942.

The designation HG.34 was duplicated in August 1941 and is shown here as HG.34A