A very fascinating photograph posted by @BMB shows a Signalling Class of 45 (Battle Axe) Company RGA. It records all the names of those on the course, which includes @BMB's great grandfather and grandfather. 

45 Company was based at the Citadel in Plymouth. The Coastal Artillery Units during the Great War acted as training locations and places where Siege Batteries were formed. Many men would therefore not stay with 45 Company RGA.

The younger Baker would be posted to the Middle East, spend time in Ireland 1920/21 and continued in service until 1926. The fact names were recorded, allowed Pals to do research as what happened to these men once they completed their course.

RGA Plymouth 1916 45th (Battle Axe) Company (all named) - Page 4 - Soldiers and their units - The Great War (1914-1918) Forum (greatwarforum.org)

The Citadel in Plymouth was completed in 1598, its function was to protect the naval facilities of Plymouth and Devonport. 

In 1860 a Royal Commission on the Defence of the United Kingdom was formed to address concerns of the strengthening of the French Navy. The resulting recommendations led to a series of forts being built at key coastal locations to address this threat, termed Palmerston Forts, named after the then prime minister. In Plymouth, these forts ringed the naval areas, and reducing the function  of the Citadel.

The Citadel became a training location and military base.

Royal Garrison Artillery 'The Citadel

The Citadel in Plymouth is still an operational location for the Royal Artillery, being the home of 29 Commando Regiment RA.

The Battle Axe Company was a nickname given to 45 Company RGA as a predecessor unit had been awarded the Battle Axe for actions in Martinique in February 1809. 

Source: The Sphere 3/4/190 courtesy of @charlie962

The Battle Axe Bombardier / Corporal would carry the Battle Axe on Parade.

THE BATTLE AXE

Source: Honour Titles of the Royal Artillery - By Major General B. P.  Hughes courtesey @FROGSMILE

Despite being a venerated object, it would seem that during the Great War it managed to be lost from it's home in a glass case in the Officers Mess, and ended up in a rubbish pile, being found 18 months after the end of the war. 

Source: Western Morning News 3/9/45 Findmypast newspapers courtesy of @charlie962

After the First World War, Battery Honour titles came in to use and the The Battle Axe Company became a formal designation for the Battery who were successors of 45 Company Royal Garrison Artillery. The Battle Axe retrieved from the rubbish pile would return to it's venerated status. 

The Battle Axe Company is a honour title that is still active in the Royal Artillery. Currently with 74 (The Battle Axe Company) Battery, a constituent of 47 Regiment RA operating Watchkeeper Unmanned Aerial Vehicles (UAV). The Battle Axe is paraded annually on 24th February.

On the outbreak of the First World War, 45 Company RGA based at the Citadel Plymouth was part of the Eastern Section (Plymouth), South Western Coast Defences. It served alongside 36,38, and 41 Companies RGA, who were reinforced by the Devon RGA (TF).

45 Company Royal Garrison Artillery

Signalling Class 45th (Battle Axe) Company RGA Citadel Plymouth 1916

The photograph of the signalling course shows the various methods of signalling available during the First World War; heliographs, flags, telegraph and field telephones.  The presence of a General Post Office Engineer brings in civilian communication expertise.