7th October 2019, Brockwell Park
Growing through grass under oak. Few scattered. Cap 1.5cm, stem 6cm. No smell. There's many Parasola species with a similar appearance, so could easily be one of those instead. ID is fairly likely.

6th September 2015, Ladywell Fields
Growing in earth amongst grass near oak tree. Two. Cap 1-2cm, stem 4cm. There's several similar species but spore shape and size seems to say this is P.leiocephala. It grows on buried wood debris which I didn't notice but could easily have been there. ID is best guess. Spores 8-9.5µ x 8-9.5µ.

Spores