As approximately two thirds of WW1 service records were destroyed during the WW2 bombing of London, researchers have to look at other surviving records that may give an idea of a soldier's enlistment date. One such set of records to look at are the registers for soldiers who were discharged from service due to wounds / sickness -- these registers are known as the Silver War Badge Records, 1914-1920. Using these records I looked for soldiers that had been discharged and that their service number was close to that of Gardiner -- my search came up with --
S6319 -- Lord, H -- enlisted 21/11/1914
S6333 -- Edwards, A -- enlisted 22/11/1914
S6364 -- Gardiner, WH
S6407 -- Sansum, G -- enlisted 23/11/1914
Cross referencing these three men to their entry in the Medal Rolls, I find tyhat all three were in the 12th battalion, Rifle Brigade. I feel that it is safe to say that Gardiner enlisted on either the 22nd or 23rd November 1914.