Liverworts along with mosses, belong to a group of plants known as the Bryophytes and grow on the surface of soil where the drainage is poor. There are about 289 species found in Britain. Marchantia polymorpha shown here, is very common in gardens and greenhouses.
The thick dark green, leafy structure (the thallus) has upward-facing male reproductive structures like toadstools and female ones develop on the underside of a parasol-shaped hood borne on stalks, resembling minature palm trees. When ripe with spores the elevated capsules on the undersides of the female structures burst open. There are also cup-shaped structures on the surface of the thallus, these produce small green granules called gammae which are dispersed by raindrops and grow into new plants - see bottom picture.

There are fine fibrous root-like structures (rhizoids) about 5mm long, in a row below the midrib on each thallus, these are for anchorage and water uptake. Because of their appearance, it was once believed that liverworts could cure diseases of the liver, hence the name.
They spread by spores which are carried in the air and by the gammae, so if the right conditions are present they will soon cover a flowerbed. If the lawn is compacted and poorly drained the grass will be sparce providing a perfect area for the liverwort to establish.
Sometimes they are found on the surface of potted plants, which can indicate that the plant has been in the container for too long, may be starved, poorly drained and the roots may have rotted or died back. Even if not present the pot may have been in the vacinity of some spores or gammae, so discard the surface compost before planting.
Without a mulch, use a hoe to keep the soil loose to about 3 to 4 cm deep. When a large area is covered the best solution is to slice off the Liverwort and apply fresh mulch.
Improve the drainage by adding grit and organic matter. A mulch of coarse bark chips should prevent establishment for a while but if it settles the spores of the Liverwort will soon take over in shaded, moist areas. In the lawn feed and improve drainage by pricking or aerating.
Winter frosts usually lift the tough growths so early spring is a good time to tackle it as it is loose on the surface of the soil.

Glyphosate will kill it, but should be applied with a few drops of detergent in the water to try to penetrate the waxy surface of the thallus.