Yes Minister is brilliant as a comedy but rubbish as a documentary. Civil Servants may advise the Minister that what they are proposing is difficult, or even impossible, but the instant that the Minister makes a decision, it is their job to implement it, and that's what they do. If you tell someone to do something that's very difficult, though, you can't subsequently blame them if they struggle to get it done.
This happens again and again. The new train timetables, that have been causing chaos, were a brainchild of the then Transport Secretary Patrick McLoughlin. That they have gone horribly wrong was no surprise to his Department, but they did their best to deliver it according to his instructions anyway. Turns out that it went badly, as was predicted -- and no, this isn't a self-fulfilling prophecy either.
Same with Universal Credit, as with Brexit (or the current attempts to implement it). Civil Servants do as they are told to, whether they like it or not, and their own personal political beliefs have nothing to do with the way they carry out their roles.
End of.