Anyone offer any advice on these formations.  Are they rare?  How do they form?  Do they have a name beyond speleothem?  Located in north of England.

Looks to me as straws with helictites presumeable aragonite.

Rare ? Depends on the region. Aragonite comes in different colours where white is the most commen. Blue and green are the rare ones

Some photo galeries : http://www.scavalon.be/webalbums/Aragonite/index.html

Aragonite??  You're in luck there.  I found this information on a reputable geological site
Looks like you'll never get vitamin D deficiency or cold toes if you spend long enough underground with those straws!


"...Aragonite is attuned to the Earth Goddess, encouraging conservation and recycling.  It is a reliable earth-healer and grounding stone.  Aragonite transforms geopathic stress.
Aragonite brings warmth to the extremities.  It combats deficiencies in Vitamins A and D.  Aragonite combats dis-ease and can stop night twitches and muscle spasms.  It also helps with general aches and pains..."

Presumably it also cures Covid (that's if it actually allows it to affect you in the first place). 

Not that rare in Mendip caves. I can think of at least three sites off the top of my head.

Similar.

Withyhill, Mendip. The op's image looks more like clusters than helectites though.