To add to the existing answer, In the Victorian era, British soldiers (both officers and other ranks) were recruited into a regiment, and normally stayed with that regiment for their whole career. In the British system, the regiment is the primary organisation that soldiers identify with, and has the trophies and battle honours. This is called the "regimental system" and it's very different from the "continental system" used by the US Army.
In the British system, battalions are deployed for combat as part of a brigade, and brigades are grouped into divisions. But the assignment of battalions to brigades and brigades to divisions is a temporary thing, and always subject to re-organisation. If a regiment has multiple battalions, it's most unusual for them to serve in the same brigade or division.
Leaving a regiment requires actively applying for a transfer, which was quite unusual in the Victorian era, or being promoted to full Colonel, at which point your regimental identity is supposed to be replaced by a branch-of-the-army identity, although senior officers tend to remain fond of their regiment.
To make it more confusing, The Royal Artillery, Royal Engineers, and similar organisations (corps) are considered to be regiments for this kind of purpose, although they are far larger than normal infantry or cavalry regiments, and may have multiple depots.
So an officer serving with a depot battalion would be serving with the depot of his own regiment. Is Hart's Army List organised by regiment? The twentieth-century Army Lists are organised that way.