We've had variations of this topic discussed here over the years. I would say that it's realistic for you to get into consulting (non MBB) with a 2.2 from Cambridge, but you're going to have to work that bit harder to get interviews.
The key is not having your CV rejected within 10 seconds because of the 2.2
That's a challenge, because most of these firms will have 100+ good graduate CVs for each position they are looking to fill, so things that help them whittle the list down to a more manageable shortlist (like poor academic grades or the wrong university) are pounced on as a reason to reject you.
I would suggest that what you need is someone inside each of the companies who will fight your corner and say you're worth interviewing. So:
Through LinkedIn research and discussions with the Cambridge careers service, find people who went to your college or who studied the same degree as you who are now working in your target firms. Then try to speak with them, explain your circumstances and win them over that you're worthy of an interview. If a consultant within the business passes on your CV to the recruiting team, your odds of the 2.2 being overlooked are significantly increased.
Better still, see if you can find out from the careers service people who've got a 2.2 in the last few years and who've successfully made it into an entry-level consulting role. This does 2 things. Firstly shows you those firms where there's a track record of this being possible; and secondly, gives you a kindred spirit within the consultancy who may warm to the idea of helping you.
"Hey Hugo. Hope you don't mind me getting in touch. I'm doing my masters, having fallen just short of the 2.1 I was aiming to get from Cambridge. The careers service said your firm have occasionally extended offers to people like me and I'm hoping to find someone there who could help me have my application taken seriously"
"Funny you should have contacted me V-M, that's exactly the situation I faced a few years ago...."
I personally would want to do all this by phone. Email or LinkedIn InMail is the lazy route - and much easier for the recipient to just hit delete. Plus you'll have a better gauge on the progress you're making.
Hope this helps in any case - and good luck
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