The message
from "Tony" contains these words:

Could it be crocosmia?

Sounds very like it, and they can make a very dense mat.

I'd get out the heavy-duty kills-whatever-it-touches Roundup and paint the
leaves with it.

Completely wrong time of year for using contact weedkillers, and even
if it was the right time, they may not reach small underground leafless
daughter-bulbs forming a new corm with its own roots, alongside the
parent one with leaves. It's a job for patient digging and lifting; but
all the UK-naturalising bulbs I can think of which still have leaves
showing at this time of year, will eventually succumb to this. Any bulb
will also eventually shrink and die, if all its top growth is cut off
frequently at ground level during the growing season.

Clearing every tiny loosened bulb visible on dug ground is the kind of
simple job that a child, teenager or student might do for financial
gain...preferably by volume of results.

Janet.