You can actually kill it off by repeated strimming for an entire season

I hard a similar approach for any hard to get rid of weeds. Sow grass seed
and mow every week in the growing season keeping it really short.
Apparently this causes the weeds to use up the energy stored in the roots
faster than the leaves can generate it. Eventually (a season or two) they
die. Then you can lift the turf (green manure?) and do what you like with
the plot.

Personally I am too impatient - I want to plant veggies in the spring. I am
digging the garden and getting out all the roots I can (nettles, couch
grass, brambles, some thing with red roots/tubers) and if necessary I will
treat with Glyphosate in the spring.

Mike