In reply to Sam Beaton:
Don't know Harpur Hill sorry and not certain as to your excellent edge holds, but with limestone and other sedimentary rocks you most certainly get other stuff sneaking in there too 😉.
Usually a bloomin' great crack/fault in the limestone or in the weakness of a bedding plane some hot stuff, often hot and wet stuff got squished through the gap and then solidified. Examples of solidified stuff include Galena/lead ore and fluor Spar (there's a lot of lead/fluor mines up Buxton way), but other minerals can cohabit with lead, such as Zinc (blende), iron ore (siderite mostly in UK and that's a sort of iron carbonate so an irony variant of limestone).
Plus look about the peak limestone and there plenty of examples of naughty intrusions of lava here and there, thinking of a few in Castleton just off the top of my head but maybe some in Buxton too?. The old Peak miners gave name some forms of igneous intrusions in limestone the name "toadstone".
Also, not an intrusion like lava, but because limestone, mudstone and shale were ancient sea beds, there's a lot is stuff in that water that precipitated out, usually in discrete layers and also sometimes as lumps/nodules or crystals. Chert especially which is a silica rich sediment, it is usually black and hard and sharp and commonly in layers in limestone, you sometimes see bands of nodules in chalk where it is really hard and gets called flint (flint is excellent at cutting ropes, beware).
While crawling/wading about underground underneath a lot of limestone on Saturday I even saw some lumps of coal in one spot, although that was in the Y Dales not Peak but mentioning as all sorts of stuff can be mixed up between the layers of limestone series.
I'd hazard a guess your solid holds are bits of chert in the limestone, but happy to defer to someone with local knowledge
Post edited at 12:50