I have a couple of "clumps" of toadstools growing on the lawn. The
biggest area of the two is probably 20 or so of the buggers, clumped
into a circle the size of a dinner plate. They're a light brown colour
but don't know what species they are or whether that is relevant.

Probably Fairy Ring Champignon.

What's the best way of removing them and ensuring that they don't
re-occur?

They'll burn themselves out soon enough. We usually get a ring or two in
the Autumn, but they don't last long and don't do any damage.

You could eat them if you want to get rid of them quicker [Disclaimer:
Get a proper ID on them first!]

Al.