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)