Where?
And
Where does it state lawfully a minimum calibre is to be used apart from The Deer (Firearms etc)(Scotland)Order 1985?
There is NO minimum calibre stated on an authorisation.
I always believed it was .270 but can't find anything that actually states minimum calibre, but this is what I have found out of date admittedly.
Red Deer Commission publication , Night shooting 1986
Red, Sika(and Red Sika crosses) and Fallow
Rifle capable of firing ammunition of 130 to 150 grain soft nosed bullets with a muzzle velocity of not less than 2450 feet per second and a muzzle energy of not less than 2250 foot/lbs, If there is any doubt about the formula prescribed above any reputable supplier or manufacturer or the Red Deer Commission should be consulted.
Roe Deer
Rifle capable of firing ammunition of not less than 100 grain soft nosed bullets with a muzzle velocity of no less than 2450 feet per second and a muzzle energy of not less than 1750 foot pounds.
This combination of rifle and and bullet gives a performance which is similar to or greater than a .243 and is the same as laid down by the firearms order for shooting Red ,Sika and Fallow deer in daylight.