Plunger plan foiled by my sink having a major design flaw. The draining board's overflow connects to the main pipe, so every plunge of the plunger merely pushed water onto the draining boad. It definitely shifted some muck out of there, but hasn't helped otherwise. The plunger's seal also isn't very good to start with (that's what I get for buying cheap junk) so it keeps bubbling back after I push it down.
I decanted the water from the sink (using a selection of bowls and jugs and then a sponge) and tried again with the plunger. Still no joy.
Mr Muscle unblocker has done nothing except make the entire kitchen stink of chlorine, so I've opened the window in there and shut the door.
Looks like we're taking the pipes apart, then.
Edit, 17.56: Oh no we're not!
I had another go when the chlorine-y smell had dissipated a bit, this time blocking the draining board's overflow with a sponge, and the plunging finally worked.