the cabinet ministers (the executive ministers of the ruling party)
A set of unelected bureaucrats, by your standards, if you think about it...
Ministers =/= Bureaucrats
The civil service are our equivalent of the unelected bureaucrat, with the civil service being neither appointed by nor elected by anyone, rather being employed on a professional basis to advise, administer or execute policy decided upon by executive branches of gov. The ministers are appointed, the members of parliament elected - though traditionally, the ministers are appointed from the house of commons (as a result, 28 of the 29 ministers including the PM are all elected members of parliament, the one minister who is not an elected MP is a Baroness of the House of Lords, who is the minister in charge of the formalities and organization of the House of Lords - her post is always held by a peer).
So by my standards they are not equivalent; different problems exist for rule by Ministers or rule by Bureaucrats
The European Commission is effectively a cabinet, which everyone complains about. The President of the Commission is suggested by the European Council and agreed upon by the European Parliament, the rest of the members proposed by the Council Of The European Union. It is non-executive in powers, so nothing like the proposed super-government Westminster cabinet in terms of powers, not even the current "need to defer to parliament" cabinet executive, as they need the EP/etc to
listen to them, not just ratify.
The European Council is composed of the Heads Of States/Government, who vary by their way they attain that power but are mostly voted in by the democratic process that the entirety of their home state already uses. (Our HoG isn't, please note!)
The European Parliament is an elected body, as per the Westminster one, with a few (arguably better) small differences to the process.
The Council Of The European Union consists of one designated minister for every state, however so those ministers are put forward.
The European Court Of Justice is composed of one representative judge from each state, but I'm no expert on how every state stuffs its judiciary.
The European Central Bank is administrative, not legislative, and composed of term-limited individuals recommended for their financial expertise and integrity by the national governments, and is much derided but is pretty much nothing like as bad as painted and irrelevant here except for completeness.
As is the European Court Of Auditors, whose composition is dictated by the Council and function is not even remotely legislative.
So, which set of bureaucrats (that, where they count, aint even bureaucrats!) has any more undue relative power than this group of people we propose to give such power to in the UK. This group appointed
only by convention from amongst elected persons. Persons elected to just one non-majority party, and chosen/made-do-with by a person whose sole practical majority is the 26,000 odd
constituency voters (down from 29k!) that lets her represent Maidenhead, and only in power 'cos she was the last woman standing and now nobody from her own party has any mind to seize the poisoned challice from her unappointed lips... Yet!
Tell me that you had
any hand in getting
any of this potentially hyper-executive Cabinet into power. At most, you might have voted for one of them, but (unless you're in Maidenhead, and even then) then that's just luck. Run the numbers, and you'll find that your voter influence in these matters is more insignificant than the multi-path authorisation that the average European (us included, although we Brits can't actually claim to have elected our Head Of Government, so maybe we should fix
that first, before complaining about the Gnomes Of Zurich, etc.) has over the pan-European supranational institution that some of us seem not to like.