As others have said, the days between interviews varies completely based on:
1) Cycle you applied on (university recruiting/off cycle / experienced hire)
In London, if you are applying during University recruiting you can expect to have 2-3 weeks between rounds.
There is no answer here. From a couple of days to 3-4 weeks. You can also reschedule the interviews if it does not suit your schedule (unless it's the University recruiting with the defined interview dates)
In the final round, I would expect a bit more structured and demanding approach to the fit part. The partners in the last round are more experienced and they will challenge every single detail of your story. So make sure that you have a couple of backup stories. Thus:
1) Make sure that you've prepared everything: A story about yourself, motivational questions and the main FIT stories. Also, don't forget about your questions to the interviewer - you'd rather have an interesting conversation and score some point instead of a simple Q&A session
2) Then go through each story and think of the additional questions the interviewer may ask. It’s important since additional questions will take up to 50% of the interview. Try to remember the main details and facts and make sure that you know how to explain the key concepts quickly. Test your stories with your friends, ideally consultants, and ask for their feedback. There can be multiple groups of additional questions:
3) Now work on 3-6 backup stories. During your interviews, you can then use these stories or adapt these stories to the additional questions your interviewer asks you.
You may be interested, why you need to prepare several stories for each question? At the end of the day, it's not that easy to come up with all of these stories. I've answered here: https://www.preplounge.com/en/consulting-forum/repating-fit-interview-stories-927#a1813
4) Next step is talking to consultants. I recommend doing a couple of mock interviews, both case+fit. You can connect with consultants via friends, company events or even LinkedIn. Consultants are entirely opened to share their experiences, but the biggest problem will be the lack of time. Sometimes you’ll need to send a kind reminder to your request, but it pays off.
As for the cases - Partners and Directors have their own favorite cases and may even want you to lead the case. The key difference:
It may seem to you that these 2 types of cases are different, however, the interviewer-led type is just a simplified version of the interviewee-led case. My advice is to always prepare in the interviewee-led format so that you could solve both easily.
It varies a great deal!
Some of my friends had 3 days - This was for a specific target university recruiting drive.
2 more of my friends had 3 months in between.
Me personally, it's been 4 weeks and counting!
If you are an ad-hoc hire expect it to be 3-5 weeks on average.
I have had clients do their second round on the same day as the first round; more often, you have a couple of weeks. Sometimes (as in my case), you have a full month.
Second rounds aren't really "more difficult", even if the expectation if that you will do better at the case interview itself. More than anything, you will be sitting in front of people a lot more senior (think senior principals/AP and Partners). At that level, the focus is more on selling and client relationship than cracking the actual case, so expect more general questions and open discussions: the objective will be to figure out if the company can trust you to build relationships and not say anything stupid in front of the client. Does that make sense?