The four lanes/basset/lanner/uny/buller/bucketts escaped operation minecap but were tackled in the 90's by Carnon, who plugged a lot of shafts but most certainly made a few deep holes safe (sadly sealing off some very interesting workings in the process). Even though a few were left open on Uny, the others pretty much all disappeared. The only few shafts that escaped the plugging programme are very oddly sited, or perhaps on private ground.
Four Lanes has got a few plugs around it, but there are patches of ground with open shafts. I would have thought that the shafts which got plugged were within a certain distance of a right of way. A few (there is a beast above basset) were left in the middle of plug zones. Having a read of the archaeological blurbs surrounding the last plugging programme, they were very thorough indeed. They dug out choked shafts and really made 200% sure they were safe. They then left others open.
There are a couple of patches of wasteland around fourlanes, which I imagine neither contain a public right of way or ownership by an agreeing party. My bet is on one of these.
Adit is pretty deep here, around the 60-80m mark (I recall), the flat lode is deep here, so there are unlikely to be any workings off. Plus, a lot of the shafts I have managed to have a crafty peer at are rubbish bins.
I don't imagine the fire brigade were particularly bothered about whether the shafts went or not, whether there was archeology or mineralisation present.