Sadly, this ideal of the Westminster system has been under attack for the last decade or two. Secrecy has been broadly imposed on the public service and non-partisan department heads are sacked and replaced with political lackeys. The ideal isn't dead though. There are people in the public service who are trying to keep it non-partisan, and those efforts should be supported rather than it all being written off as a hopeless case.
[1] https://sef.psc.nsw.gov.au/nsw-government-context/the-westmi...
Westminster type systems are arguably hybrid oligarchies. Australia is a good example - look how it continues to function in largely the same way, on largely the same trajectory, despite having 5 prime ministers in the last 10 years.
Your original comment had truth to it but bundling the BBC in undermined that, however you define it here.
"Public Service" is plainly a positive term though. It lends an air of altruism. Not particularly interested in what nomenclature is standard (according to who? 7 etc etc).
"Official state media" is more correct