You strim it back as close to the ground as possible then apply a solution of salt and white vinegar. Cover the area in black plastic or that weed suppressor material.
If you don't mind the chemical route then glycophosphate or I have heard it suggested bleach will work too.
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Currently sharing garden with - Moles, voles, rabbits, pheasants, sheep, cat, dogs, hare, buzzards, crows, slugs, frogs . . . . .
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