Err, L.S. Power, I think you've got the dog by the tail there, matey, if you're talking about scheduled airline ops, anyway.
Perf A aicraft have to meet certain climb criteria with an engine out before they're certified. (No, I can't remember what they are, though 2.5% for 3 and 4 engined aeroplanes rings a bell). Provided you adhere to the performance criteria (WAT limits etc) you will clear all obstacles within an expanding cone based on the departure end of the runway if you continue straight ahead, unless there is a close-in terrain constraint that intrudes into that defined area,in which case the airline ops. dept. must establish an emergency turn procedure.
SIDs will obviously keep you away from the terrain, but that's not their primary function - can you think of any terrain constraints to the west of LHR that necessitates an early turn left or right? Those LHR SIDs are there to keep you away from other traffic (and the local MP's house
). Of course some SIDs do have terrain constraints to consider and these often show up as minimum climb gradients to certain altitudes, or a requirement to remain visual to a certain height or somesuch.
Hope that helps.