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Or is the the Civil Service filtering recruits, the flyers going to Treasury and FCO whilst those who didn't even make HO end up in DWP?

Haven't you heard? It's "assorted weirdos" to the top of the pile

https://dominiccummings.com/2020/01/02/two-hands-are-a-lot-were-hiring-data-scientists-project-managers-policy-experts-assorted-weirdos/