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.

thallose liverworts	leafy liverworts
Conocephalum conicum	Pleurozia purpurea

Leafy liverworts nearly all belong to the order Jungermanniales. Thallose liverworts belong to one of two orders: Metzgeriales and Marchantiales.

Useful links:

British Bryological Society