Added a picture of the tap. May get round to a video (can't do it now)
The only faucets I’ve ever seen without an aerator are the basin farm-style spigots that have become a recent fad. All others should have one equipped when sold. That’s an important distinction to make because many people remove them without replacing them, usually due to poor pressure or not wanting to be bothered to go buy another one. Your faucet could be missing one for that reason.
The bathroom tap downstairs clearly has an aerator, but it's a completely different model.
Only on the cold, though I almost never use the hot.
I'll look at finding a wire or sth. I reckon I can take it from here. Thanks for your help.