Since you are applying as part of the regular graduate hiring in London, the scheduling of interviews/tests is not aligned to when you submit your applications, but rather when the applications close. For MBB, applications close in mid-late October for London graduate hiring cycle.
1. Online tests will be sent 1-2 weeks after applications close (so early November). Only McKinsey and Bain have tests, BCG has a GMAT-like test you do in person as part of the first round interviews (if selected).
2. First round interviews for BCG and Bain are held in ~mid November. BCG has an additional second round, which is held around 1-2 weeks after first round. Finally, BCG and Bain both have final round in early-mid December. Outcomes are communicated only after all interviews have taken place - so from your final round interview, you can wait anywhere between 1.5 weeks to 1-2 days.
McKinsey is slightly different, and just pushes schedule back a bit. PST is done at around the same time as the first round for BCG/Bain. First round interview is done around the time when BCG/Bain have final round (early-mid December), and final round is held in early January. Up until last year, final round is held in a hotel just outside London for 2 days, including a day of presentations + "get to know you" dinner.
Another difference between McKinsey and BCG/Bain is that with McKinsey, outcomes are communicated a few days after interviewing, whereas for BCG/Bain, outcome is only communicated after all candidates have completed interviews for the round.
Hope this helps!