I believe, SIDs are 'only' for all engine situations (lets consider twins). The gradients are quite high (>3percent). A SID 'may be' the Engine Out SID (operators should verify this considering obstacles). Otherwise, we should fly straight ahead (no obstacles), or, the Emergency turn (EOSID - airbus) - a flight path that has considered obstacles, and adequate clearance is assured (calculated) ONLY on this 'emergency turn' flight path with the engine out!
Yes ATC will have to be informed ASAP (after the aircraft is flying safely under control).
TR3 - know the website for CAP 385?
What does ATC think about this? Varied thoughts there!
Thanks.