Broken click clack (pop up) plug for the sink

Golden_Glow90

I'm hoping someone can help me.  I have a click clack plug in the bathroom sinks but they've rusted with time and get stuck every time I push them down.  I used a pair of pliers to unscrew one of them but the other one snapped and crumbled as I was trying to remove it so now I have nothing to grip.  Any ideas how I can remove it?  I thought about unscrewing the pipes underneath and using the pliers to get it from there but unsure if that would work, plus it's very difficult to see what I'm doing as we have a pedestal sink which is sealed at the top and bottom.  Any help would be greatly appreciated.  I've put a link to the type of mechanism it was in case that helps: https://www.amazon.co.uk/gp/product/B07ML61H4S/ref=ox_sc_act_title_1?smid=AXYFGHN78VBIF&psc=1

nofoollikeold

I'd suggest you remove the whole waste fitting, get a replacement (basin waste fitting) and get one with an ordinary plug on a chain.  Have a look at https://mcalpineplumbing.com/waste-outlet-fittings/basin-wastes
Waste plugs come in the following types:
1. On a chain.  Nothing to go wrong, but your basin may have no attachment point for the chain.
2. "Click clack" - the sort you have.  Rarely last much longer than a year or two.
3. Flip over.  Fairly good, but the seals tend to go eventually.
4. Pop up.  Generally pretty good, but your tap must have the necessary hole and push rod.  I'd guess your's hasn't.