It is "snow in summer".....cerastium tomentosum. The tatty brown bits are the dead flower heads so if you trim those off, the plant will bulk out and look a lot better in a short time. It's a great ground cover plant and doesn't mind hot sunshine.
I whack mine back to the ground every year after the flowers finish (and pull it out where it's spreading too far) and it always grows back nice new foliage. Admittedly it took a while longer than normal last year in the drought, but it was back to normal this year.
Doncaster, South Yorkshire. Soil type: sandy, well-drained
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