Findmypast has Royal Tank Corps enlistments 1919 to 1934
There is an Albert Miller 7816566 born 1894 with mother Annie, resident Nunhead.
Regiment to last posted 5th Dragoons. There is a little more info too.
Well that is definitely him, and it confirms that he came from the Machine Gun Corps (which is also mentioned on his discharge certificate "M G C Cavalry").
I think he could be the Albert Miller who served in 1st Dragoon Guards (7005) and transferred to the MGC (Cavalry) in 1917 (100473).
Albert Miller 7816566 was discharged to Reserve in 1920 which could explain why his service record is not listed by the MoD.