On the MIC's at the TNA site there are two John Cousin's both with the middle initial of W. who were serving in the Army Service Corps (one a Private the other a Driver). There is also a John H. Cousins who is noted as being a Driver in the R.A.S.C. Checking on the surname Cozens there are three that may fit (that is if the surname was spelt as Cozins rather than Cousins, as you pointed out it had already happened once so it may have happened again), John T. Cozens a Private in the ASC and John R. Cozens a Driver in the ASC. Intrestingly there is a Sergeant John Cousins who served in the
13th London Regiment which was based in Kensington. The A.S.C., the R.A.S.C. and the 13th London Regiment all resemble the cap badge in the image, however where the A.S.C. & the R.A.S.C. both have a crown at the top center of the badge the 13th does not and has an eight pointed star. I would suggest that, if at all possible, a trawl through the service records on Ancestry or FMP would be in order starting with the 13th London one first.