Yes, Minister is heavily out of date, however.
The modern shows focus on political parties because these are what increasingly have driven government, with the civil service increasingly subordinated to party interests. Policy development, for instance, is now heavily transferred to party operatives (hence Malcolm Tucker as an enforcer) rather than ministers working with their civil service departments. Civil servants simply do not have the sort of power that they did in the days of Yes, Minister, nor in fact many ministers either. This is why The Thick Of It matters, because it reflects a changing way that government started operating.
In fact, I think it's a fair point that the current British government, presently, does not really govern at all, starting around David Cameron. The Tories, ideologically, do not r
think the government should do things: the invisible hand of the market should. Thus heavy civil service diminution, deregulation, with functions handed out to quangos and agencies. Ministers then operate what is designed to be a PR machine to earn short-term favour for electoral victory. What ministers want is absolute autocratic power to make things happen, which they only use for headline-grabbing. I cannot help but wonder if the problem facing Rish! is that he realises that post-Brexit the government does actually need to govern, it's just his wider party no longer thinks that way, has any practical ideas, or is ultimately capable of doing so.