Quote from wikipedia regarding No 1 dress
'The peaked cap is not worn by all regiments;
berets are worn in lieu by the
Royal Tank Regiment,
Army Air Corps,
Parachute Regiment,
Special Air Service and
Intelligence Corps' as I said it is from wikipedia so take it as you will but it is purporting to quote from
'British Army Dress Committee (August 2005).
Joint Service Publication 336: The Defence Supply Chain Manual.
Vol. 12, Part 3, Pamphlet 15 (3rd edition ed.). p. Annex A.