Hey there, the current process in London this year was as follows:
Step 1: Submit online application
Step 2: Go into McKinsey office for two tests: the PST and a new "computer based assessment". I have spoken to candidates who did this and they said it was a series of questions structured like a game that tested your problem solving skills. One question was something to do with being on a desert island and having to come up with the right balance of populations of different animals to ensure the ecosystem remained sustainable. As a difference, the PST also tests commercial awareness, while this test seems to test "pure" problem solving ability.
From some friends at McKinsey, I understand they are testing out this new evaluation method in a couple pilot geographies (London being one of them) and comparing scores to PST. It may be that, if the trial is successful, this online test may replace the PST altogether in a few years.
Step 3: First round interviews, 2 interviews with associates/EMs. Both interviews are PEI + Case interview
Step 4: Final round interviews, 3 interviews with Associate Principals/Partners. Interviews should also be PEI + Case, but partners have some more flexibility in how they give the interview so likely to be less structured.
I am not 100% sure on the Milan process but it should be similar, minus probably the computer-based test. Note as well that there was no SHL/online test this year, which is a change from last year.