For what it is worth, there are 55,000 EU "unelected officials" (civil servants) whereas the UK has 393,000 unelected officials.
In the UK, when a change is made the government of elected officials vote first on an item of headline policy (e.g. we are going to cut the budget for flood defences by x% or invest in training more pharmacists or create a new scheme to get 18-25yos into work) - then after the vote the civil servants get started creating the full workable policy to actually decide which rivers are going to be left without flood defences, which universities are going to be given more resources to expand, which rules and sanctions are going to be applied to the new schemes - there are a lot of complex decisions that need to be made by specialist professionals who know all the facts and have been working in the sector for years rather than a minister who was working on pensions before the last reshuffle but will be in health after the next reshuffle. Civil servants often have utter nightmares getting a system that actually works and does what the government intends because the legislation doesn't have to take into account such trifling issues of practical feasibility if it doesn't want to.
In the EU the difference is that the civil servants come up with a workable practical plan for something that is needed before the elected legislative body debates amends and votes upon it, so that the elected representatives are able to understand the full implications of the new system before they vote rather than voting for something in principle before the details are all known. Arguably more efficient in terms of workload being paid for by taxpayers but not fundamentally less democratic.