Cordyceps militaris, (above) not as thick as the first one, but from the same lawn, a very shaved, mossy, unfertilised one at Saville Park. I’ve dug it up, and will search for the caterpillar when I have time.

Kuenheromyces mutabilis,  (above and below) Velvet Toughshank or Sheathed Woodtuft – same garden on a crabapple tree. This is edible – good, but only if I’ve identified it correctly ! ( Thanks to Malcolm Greaves, I correct the id to Flammulina velutipes, Velvet Shank. It’s quite a common winter mushroom.
Of course it is, thanks Malcolm. There seems to be an error/ ommission in Phillips’s index, which doesn’t help me memorise this one. I knew it was an edible one – the one that can freeze. Steve.)