"How many unelected Bishops (as an example of unelected persons) are there in a UK government?" would be a better question.
In fact, an even better question would be "how many unelected persons are there in a UK government?"
The answer being "about 800 in the House of Lords alone".
Then don't forget the judicial arm of the UK government.
Then don't forget the civil service function in UK government.
Then don't forget the Royalty.
I suspect the true answer to the question "how many unelected persons are there in the UK government?" might be a number beyond your comprehension, based on your ability to count numerous and arrive at zero.
One excellent example was presented in one of the links I provided. Clearly you haven't read it, or refused to recognise the direct comparison:
"The most powerful EU figure by far, is the President of the EU Commission (
the EU’s Civil Service), who is nominated by the European Council."
Malcolm Turner
Another of Malcolm's example:
"a prime minister who was only elected by Tories in Maidenhead, a town which also voted to remain in the EU?”
How undemocratic is that!
Another of Malcolm's comments:
"Britain is 14th out of only 19 considered to be full democracies."
View attachment 154690
http://www.eiu.com/Handlers/Whitepa...017.pdf&mode=wp&campaignid=DemocracyIndex2017
You may notice that apart from 3 other non-EU countries, the top 15 is dominated by EU/EFTA countries.
In fact of the 19 full democracies, only 5 are not EU/EFTA countries.
Therefore, it is safe to say that EU alignment or close association encourages full democracy.
But if you wish to persist in your ridiculous stance that having unelected people in government reduces the democratic legitimacy of that government, then in your opinion there are no democratic governments. Your apparent argument that unless the government is "government by referendum" then democracy is not possible to achieve, is nonsense.
Perhaps you need to remind yourself what constitutes a full democracy:
"What else does a well-functioning democracy need? A free and independent media, independent courts, limits to officials' discretion and regular electoral processes are all essential to a robust democracy."
https://www.theglobeandmail.com/opinion/government-by-referendums-is-not-democracy/article30798029/
Do you see anything in there that suggests a full democracy should not have unelected people?