To state the obvious customs and police notification is (presumably) only required in respect of the in bound flight - no need to report you are going.
I can't give a definative answer in relation to customs. I had assumed the same as yourself in relation to customs, but the wording on the GAR seems to suggest differently in relation to non EU countries.
In relation to police, you most certainly do have to give notification for both inbound and outbound flights.
The reference is Terrorism Act 2000, Sch 7, Section 12(1)
12. - (1) This paragraph applies to a journey-
(a) to Great Britain from the Republic of Ireland, Northern Ireland or any of the Islands,
(b) from Great Britain to any of those places,
(c) to Northern Ireland from Great Britain, the Republic of Ireland or any of the Islands, or
(d) from Northern Ireland to any of those places.
dp