Mid-career from State Dept. to MBB London

Hi all, I'm relatively new to the consulting application process, and while I've been doing a lot of reading and watching YouTube videos and the like, I'm still trying to get a sense of whether applying to MBB is realistic for me and also looking to get some clarity on how to format my CV. My stats are as follows:

- American with right to work in the UK, already living in the greater London area.

- Previously worked as a diplomat for the U.S. Department of State (basically our version of the Foreign Ministry, for anyone not familiar) for a decade. My career focus was consular affairs, so things like passports, visas, preventing fraud, malfeasance, human trafficking, and the like- lots of managing teams, lots of interfacing with the public, and a lot of logistical work in terms of moving people through the visa process and physically through our facilities. I served at embassies and consulates in four different countries (and received intensive language training before each posting).

- No Ivy League/Oxbridge background, although I'm not sure if that matters as much as a mid-career applicant. Also no MBA, although I hold a Master's in Politics from a Russell Group university.

So, to my questions. First, is my background something that would be of interest to an MBB firm? I'm particularly interested in McKinsey after a really positive conversation with a fellow former diplomat about his experiences there, but I plan to apply to all three. Secondly, I keep seeing guidance about how to format a CV for MBB, but most of it is coming from a US perspective. Here in the UK, CVs are generally much longer (think multiple pages including a person's entire work history). If I'm applying to the London offices of these firms, would I be better served by taking an American approach and making my CV as succinct as possible, or should I submit a longer CV, as would be typical here in the UK?

Thanks in advance for any advice!