There are nearly 300 species of liverwort in Britain. They can be divided into leafy liverworts with a stem and leaves and thallose liverworts with no distinct stem or leaves. Leafy liverworts nearly all belong to the order Jungermanniales. Thallose liverworts belong to one of two orders: Metzgeriales and Marchantiales.

thallose liverworts	leafy liverworts
Conocephalum conicum	Pleurozia purpurea

Useful links:

British Bryological Society