For DIY - this is also a placeholder.
Replacing an aerator is a trivial process on most faucets. It usually involves unthreading the aerator from the faucet where the water comes out and places like home depot or other big box stores sell all popular shapes and sizes. Replacing it takes a couple minutes.
If by sputtering, you mean air escaping, however, that would be another issue entirely. Air being introduced into your plumbing means you could ha e a serious issue upstream.
Is this the only valve you have that sputters?
I believe it's the only one. It's only recently started to sputter. It's like the water supply gets blocked momentarily.
Do all taps have aerators? The water on this tap - when it's behaving itself comes out in a solid stream, not like a shower.
Ah, maybe it's a laminar aerator. I can't see any such thing on the tap. I'll try to get a photo of the tap.
A photo or video would be very helpful, vid moreso since we could hear the whistle and sputter.
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.
Added a picture of the tap. May get round to a video (can't do it now)
The bathroom tap downstairs clearly has an aerator, but it's a completely different model.
That style(Victorian) does not have an aerator in the spigot itself, so we can rule that part out.
You can, however still have a screen in the connectors of the supply lines.
Does it only happen on your cold tap on that sink or does the hot behave oddly as well?
That tap is very easy to rebuild. My guess at this point is that you have some corrosion or deposits in the faucet causing the behavior. If snaking something like a zip tie or wire into the mouth doesn't result in removal of anything, I'd consider pulling the tap apart(after shutting the water off and releasing the pressure). There's really only a couple rubber seals in it that are the consumables, the rest should be able to be reused after cleaning.
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.
Coming out at an angle suggests that there might be deposits stuck inside the aerator. Sometimes this is as easy as unscrewing the aerator and removing the rocks and sediment found inside.
The sputtering and loud knocking noises suggest there's a bubble somewhere in the plumbing in the walls that is causing a water hammer. One possible way to clear this bubble is to fully open all plumbing fixtures at max, which will create enough water flow to push a bubble out. It's kinda like burping the pipes. You should do this with all aerators removed.