> Britain's Prime Minister is the elected MP for the Maidenhead constituencyBritain's PM is technically a Royal appointment, nobody ever gets "elected to be PM". By convention, the party leader winning at the last election is nominated, hence bringing some democratic legitimacy to the role. However, whenever someone else gets the job in unorthodox ways, like May or Brown did through changing equilibria in their parties, such legitimacy is clearly lacking. The only way we have to express that situation is by saying that the current PM is "unelected", and the PM is supposed to rectify this state by calling for a general election where he or she will obtain popular legitimacy.
Anyone following UK politics for more than 10 minutes knows perfectly well how this works, and trying to fight the definition through pedantry is, by itself, a partisan statement.
> The EU on the other hand has a so-called "Parliament" which cannot propose legislation
But it can veto it, blocking anything they want.
> cannot amend legislation
In practice it does, through the various committees "helping" the Commission.
> cannot repeal legislation
That is a problem, but it's not terrible in itself; a Parliament who'd want a certain directive dropped would express a popular will that the Council would likely share; which in turn would make the Commission prepare a superseding directive.
> It has neither "Government" nor "Opposition"
In practice it does. The Commission President is the candidate of the party winning the largest amount of seats, and the Parliament President is the candidate of the runner-up party. The most popular party will naturally be in government in most countries, hence dictating the agenda in Commission and Council. The Parliament can try blocking legislation, much like a national opposition would do.
> being essentially a rubber-stamping body
That's unfair. Directives can change quite dramatically when going through committees; in some cases, the final result is almost the opposite of what was first introduced, to the horror of commissioners who then drop them. The stats about votes don't reflect the fact that, since veto powers were introduced in 2009, directives without Parliament support simply don't come up for a vote, because every vote against the Commission weakens it. Much like a government would do...
> the unelected EU Commission.
The Commission President is an elected MEP who is nominated as candidate by the party before the election; and the Commissioners are nominated by elected governments through the Council.
> what happens when that unelected group [...] starts to act in ways even more harmful
You leave. Any member state can leave at any time by triggering the famous art. 50. The EU has no army to stop you from doing that.
Of course, if your own national elites don't really want to do it, that's a problem; but that's a problem with your national elite, not with "European tyrants".