After the end of the Second World War, the allies were to permanently garrison troops in Berlin for the next fifty years. The British military contribution was known as the Berlin Infantry Brigade and was to be based in the city from 1953 until 1994. The Berlin Infantry Brigade was formed in October 1953 out of the force called “Area Troops Berlin” and consisted of some 3,100 men in three infantry battalions, an armoured squadron, and a number of support units. Its shoulder sleeve insignia was a red circle over a black background with the word Berlin in red on a black background running around the top. It is this badge that we have today, painted onto a wooden plaque:
These plaques were common souvenir items for troops garrisoned in Berlin, and were also used as gifts for dignitaries from other units and militaries visiting the Infantry brigade.
The Berlin Infantry Brigade was not initially part of the British Army of the Rhine despite being based in Germany. However, it is recorded, at the very least, by the mid-1980s, that the brigade was indeed part of BAOR, being its second major component after I (BR) Corps. One of the most interesting features of the Berlin Infantry Brigade was its attached armoured squadron. The tanks deployed to this squadron were painted in a unique camouflage pattern of white and grey square blocks to better match the urban surroundings in which they were deployed. How effective this camouflage would actually be is open to debate, however it was a popular and distinctive colour scheme and remains popular amongst modellers and military vehicle enthusiasts who like to replicate it. Here we see the Chieftain tanks allocated to Berlin on parade during the Cold War in the camouflage. Note also the badge of the Berlin Infantry Brigade being displayed in a very small badge on the mudguards of each tank:
Tales from the Supply Depot 
I served in Berlin from 1984 to 1994 as an all arms Russian interpreter attached to 2nd Regiment Royal Military Police (my cap badge was Royal Regiment of Wales). Sadly, by the time I was posted in, the Berlin Brigade shoulder flash had been discontinued for British soldiers. However, 248 German Security Unit, consisting of locally recruited Germans as armed security guards and a sub unit of 2 RMP, still wore them. So, when, after the “Fall of the Wall” I was able to volunteer as a Serbo-Croat military colloquial speaker to serve with the British contingent of UNPROFOR in Bosnia-Herzegovina, I scrounged a couple of shoulder flashes to wear on my combats in theatre. Once, as part of a team monitoring Serb artillery positions on the mountains above Sarajevo following the ceasefire, a Serb colonel harangued me over this flash, claiming I was in league with German fascists, intent on exterminating the Serb race!
The symbolism of the brigade flash is the Berlin Brigade, the black circle, surrounded by the red communist hordes. When I participated in a tripartite exercise simulating the balloon going up and WW3 breaking out, it was clearly and quickly shown we didn’t have a snowball’s chance of hell of surviving!