What a lot of waffle. To answer the original question,as far as the CAA are concerned in CAP 385,for Perf A aircraft, if an engine failure occurs after V1 then take off must be made and Vr will be made before the end of the runway, after which acceleration to V2 and the screen height will be made by the end of the clearway.The actual definiton of V2 is "The target speed to be attained at the screen height with one engine inoperative, and is used to the point where acceleration to flap retraction speed is initiated".
Obviously Company procedures may have a slightly different interpretation, but that's it from the horse's mouth.