Hello Fanxiyi,
Dont worry about BOAC,you can get his expertise with the search option when he is in a non responsive mood
VEF is a speed at which the engine is failed during calculation of take off distance by the manufacturer.
V1 is relevant to pilot as it is the speed at which the first action must have been taken (ie thrust idle) during a reject call.
The AFM has some extra reaction time (2secs)as during test,the pilots know they will reject.
V1 is therefore a speed of first action,to achieve this VEF is normally 1sec before V1 and includes speed increase from VEF.
Tests are done for VMU and VMCG/A for controllability checks during certification.