McKinsey have stated that they will be notifying candidates of the outcome of their application (invitation to 1st round interviews if successful) by 1st November, so in the next 2-3 days. BCG said that they'll be sending out the results of the online application in "early November." Bain & Co. sent out their online SOVA assessment already, and it was due on the 28th Oct. They haven't said when they'll be notifying candidates of the outcome, but according to their email, their first round interviews for the London office will be taking place 12th-20th November, so I presume they'll also communicate their decision early Nov.
My trainees already interviewed/received job offers from Bain ME offices in the past few weeks (for post-MBA roles). Thus, I believe that you should be receiving the outcome of your application soon.