I scanned some organization tables from my Cold War encyclopaedia today and I figured I may as well post them here because they're pretty interesting. These are all from the early '80s. Some of the scans are a little wonky unfortunately.
The 1 BR Corps was the Army corps part of the BAOR stationed in Germany.
The UKLF are the land forces, as the name might suggest, based in the UK. These are still meant to reinforce the BAOR or other flanks in case of war. 5 Airborne for example served in the Falklands.
These are the armoured divisions part of the 1 BR Corps. Note the 3rd Armoured Division doesn't seem to follow this layout.
These are the Armoured Regiments found in each Armoured Brigade. Note that the usual Armoured Regiment is a Type 43 (for 43 tanks) and not the Type 57. The Type 57 just has an extra armoured squadron. Also note that there is no such thing as an Armoured Battalion, it goes squadron to regiment.
Also found in the Armoured Brigades are these Mechanised Infantry Battalions. There were no Mech. Inf. Bat. present in the UK.
As well as these Armoured Reconnaissance Regiments.
And these are the Royal Engineer support units, also in the Armoured Division.
There is also the two not mechanised infantry battalion types. The Type A is in wheeled Saxon APC's (presumably Saracens before the Saxon). The use for these Saxons was mostly transport from Britain to the BAOR, and thus I believe that these Type A's were based only in the UK.
The Type B Infantry Battalion was purely used for Home Defence, and thus found with the UKLF and not the 1 BR Corps. They are equipped purely with soft-skinned vehicles like Bedford Trucks and Land Rovers. They have significantly reduced anti-tank strength but do have discount engineers in the form of assault pioneers.
Also based in the UK is their own Tracked Armoured Reconnaissance Regiments. Probably mostly used by brigades that had the Type A infantry battalions.
There is also the not tracked variant, presumably used with Infantry Battalion Type B. They're mostly Scorpion and Fox based, as opposed to the Tracked version that gets Scimitar and Strikers.
There is also the Yeomanry Reconnaissance Regiments, both BAOR and Home Defence. These supported Territorial Army units.
Not included here is the many other British units stationed around the globe other than West-Germany and the mainland UK.