There have been two formations named British Army of the Rhine (BAOR). Both were originally occupation forces in Germany, one after WWI, and the other after WWII.
The second BAOR was formed on 25 August 1945 from 21st Army Group. Its original function was to control the corps districts which were running the military government of the British zone of occupied Germany. After the assumption of government by civilians, it became the command formation for the troops in Germany only, rather than being responsible for administration as well.
As the Soviet threat increased, BAOR became more responsible for the defence of Germany than its occupation. It became the primary formation controlling the British contribution to NATO after the formation of the alliance in 1949. Its primary combat formation was I Corps. The commander of the BAOR was also the commander of NATO's Northern Army Group NORTHAG in the event of a general war with the Soviet Union.
The North Atlantic Treaty Organisation(NATO) was formed in 1949 and the field formations of BAOR, expanded to four divisions, were placed under the command of Northern Army Group in the central sector of Allied Command Europe.
In BAOR for the first time an entire Signal Regiment was formed for tactical EW, 14 Signal Regiment, in 1977.
The end of the Cold War led to the disbandment of BAOR in April 1994, but British troops remain in Germany in reduced numbers, with new tasks, under command of the UK Land Force HQ in England.
BAOR was the main peacetime element of the British Army from the end of the Second World War until 1994, with the bulk of the Army based in Germany prepared to counter aggressive Soviet armoured attacks.
BAOR was constantly exercised to ensure its readiness in time of a crisis.
BAOR was disbanded on 28th October 1994 with the Prince of Wales paying final tribute to the Army, as a parade of soldiers from the Queen's Dragoon Guards and the Devonshire and Dorset Regiment lifted their caps and roared three cheers for the Prince as he took the last salute from the troops.