The Special Branch requirements are contained in the Terrorism Act.
Specifically Schedule 7, Section 12.
SCH7(12)(3):
(3) Where an aircraft is employed on a journey to which this paragraph applies otherwise than to carry passengers for reward, the captain of the aircraft shall not permit it to call at or leave a port in Great Britain or Northern Ireland unless-
(a) the port is a designated port, or
(b) he gives at least 12 hours' notice in writing to a constable for the police area in which the port is situated (or, where the port is in Northern Ireland, to a member of the Royal Ulster Constabulary).
Permission is required where passengers are being carried for rewards.
No mention is made of the aircraft registery. It is simply "an aircraft". Therefore it would apply to G reg, N reg, F reg, EI reg etc...
The Terrorism Act itself can be found by clicking here.
Customs requirements are obviously additional to this.
dp