UK Fungi

A nice find of Cuphophyllus ledidopus - Scalyfoot Waxcap
In sheep grazed pasture near Rochdale.
This young one has much clearer scales than I have seen before.

The salmon flush to the gills is a good indicator but quieta is often pure yellow so keep in mind the dry and often widening stem and the emarginate gill attachment. And the smell, which I think of as smelling like an engineering workshop, seals the deal. Sometimes these smells take a bit of coaxing...

The difference between cercacea and chlorophana can be obvious or more subtle. Adnate to decurrent gills in ceracea and adnexed gills in chlorophana is the simple difference. Sometimes it's not that obvious. Chlorophana, cap usually opaque and quite slimy. Ceracea cap often translucent and striate w...

The final image is of H. quieta. Your description also fits with this species.
The first two appear to be H. chlorophana. That would not have a dry cap and stem.
The third image also appears to be chlorophana but without seeing the gill attachment is difficult to know.

This one parasitises Galerina, probably pumila.
The stouter one, paradoxum, parasitises Cystoderma amiamtheum. As does pearsonii which I saw last year.
Yes, another name change, previously Squamanita.

Dissoderma contortipes
Found at two locations on good waxcap grassland site in the Peak District.
Shown alongside D. paradoxum, also prevalent at the site.
Spores subglobose 5.5 x 5

Black marks at cap edge suggest Hypholoma

Directly around York isn't great as it's largely agricultural. However you don't need to go far to see good waxcap grasslands. I've recorded over 40 species of waxcap in Calderdale along with the associated Clubs, PInkgills, Earthtongues and allies. You could contact NEYEDC who are identifying waxca...

Have a look at Abortiporus biennis, Blushing Rosette

I think these two species are currently considered to be the same.
http://nefsg.co.uk/lycogala-epidendrum-sensu-lato

The colour in the caps fades over time. It looks to me like yours have just faded.
They can have quite orange caps and you can rarely find pure white ones.

I don't think this is a fungus.
More likely it is the remains of a predated amphibian.