In the case of the BOAC 707 GARWE - I recall the fire handle was never pulled which, amongst other things, arms the fire extinguishers hence the reason why the fire continued.
From wiki:-
The crew's omitting to shut off the fuel to the engine was blamed for the rapid growth of the fire and the loss of the aircraft.
This was a long time before CRM etc - the correct accomplishment of the fire drill was entirely on the shoulders of the Flight Engineer who was, I believe, on his first trip not under supervision.
One result of the inquiry was that when the fire drill was read after the memory items the Captain was required to also check that the fire handle had been pulled.
One aspect which I don't think has been mentioned in all suggestions of urgency to land that, in the event of various parts departing the aircraft, it might be prudent to do a low speed handling check at height - you don't really want to find the aircraft departing in roll (say) when you extend flaps on the approach with less height available for correction and recovery.
There are very few cases (like -WE) where you need to get back down on the ground ASAP. If you are not sure what to do it's often better to sit on your hands and do nothing (other than safe aircraft control) before regretting hasty action.
Well done to all crew, ATC and emergency services.