The message
from Kay Easton contains these words:

Grass
is an excellent coloniser of bare ground and will happily work its way
through any edging you put there. I'd suggest devoting an area to
'vegetable garden, surrounding the whole thing by a wide path, and
keeping grass well out of the veg garden.

I'd second that. At my last garden we completely surrounded the veg
garden perimeter with a path made of 2x2 concrete slabs (free, 2nd hand)
and it made a huge difference to the weeding. Advertise locally and
you're sure to find someone who's getting their driveway re-done with
natty paviours and is desperate to have the slabs taken away.

Janet.