Terrible Weeds Facing Sea

by Dr.R.L.Symonds
(Broadstairs, Kent)

We are in Broadstairs, North Foreland, facing the sea, on a thin chalk soil.

The weed spreads everywhere and seems impossible to eradicate by digging.

It resembles wild garlic (Jack-by-the-hedge), with multiple small white flowers, but does not smell of garlic, though obviously an Allium. It multiplies by division of the bulb, forming bulblets only a few millimetres diameter, growing up to a centimetre diameter. Picture attached shows a fully grown one on A4 paper.

Any ideas on eradication?