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Is there anything which I can use on my vegetable patch which will
kill all ground-living insects ?

If the pests are blackfly or greenfly then you could use sprayday or bug
clear.
If its carrot or cabbage root fly then there is no chemical treatment
available on the amateur market. Instead you would have to grow resistant
varieties or put up a one metre (3 foot if you prefer) high barrier. Fibre
fleece could also be used.