Starting Master's degree in a month. Any tips for Consulting recruitment?

Why do you think you don’t stand a chance?

My profile wasn’t too dissimilar to yours (total unknowns for undergrad/masters, but had a phd and some good work experience and now at Bain). With a 1st in undergrad and (hopefully) another 1st from your MSc, you’d be just fine for grad recruitment if it’s indeed a good university 

My advice is:

• Make sure to polish your CV (1 page max, use a standard template, no fancy formatting)
• Get involved in extra curriculars left and right, and get some sort of position with them (eg treasurer, president)
• Showcase any and all achievements (you placed in a chess competition at 13? Add it. You played football in high school and won a regional tournament? Add it)
• For your existing work experience and extra curriculars in undergrad: (1) focus on the outcome of your work and not the process / task, (2) be punchy in your bullet points, (3) quantify where possible or add some qualitative metric (eg Helped reduced costs by x% in Y weeks, or most junior team member entrusted with project mgmt responsibilities)

Happy to chat some more if you want, but don’t give up before trying!

edit

Forgot to answer your questions at the end of your post (sorry, I was on my phone earlier and didn't see them):

• Cover letters: I don't know about other firms, but we don't read Cover Letters at Bain London (I know that directly from our recruiting team)
• Tips for interview process: I will link some other answers I have posted in the past, please note that others have also provided excellent responses to those (e.g., Parmesan123123, FinnesseGod, Canadiens16, StratCo), so check them out too
  • Link 1 (prep)
  • Link 2 (casing)
• General advice: same as above, some older comments I wrote (and again, check other responses too, some really good ones from the folks I mention above)
  • Link 1 (work tips)
  • Link 2 (more work tips)
  • Link 3 (discussion on consulting + day in the life)
  • Link 4 (Bain London general)