I think the full switch lands at the end of September, but already some of the Waitrose Essentials items are going out of stock a lot faster than they used to; the limited depth of stock for these items has served to remind me which items I purchase regularly that are Waitrose ones and for which I need to see if M&S has a suitable replacement, so far it has been mixed results for me. You can also find some M&S items entering the inventory if you scroll down past your favorites. I am expecting to see a lot more M&S items get pushed as discounted flash sale items at checkout over the next few weeks so that M&S can get some of these replacement items marked as favorites in your account.
Ocado are switching to M&S (from Waitrose) within the next month or two.