...cover the whole lot with black plastic for a suitable
time, to kill everything (field beans and weeds) then remove the
plastic and plant my vegetables in the weed-free soil.

I think that you'd need to leave the plastic in place for at least a year
for this to work. If you remove the plastic in time to plant anything in
spring then there will still be time for weed seeds to germinate and for
perennials like bind weed to grow.

--
Hayley
gardening on clay in Somerset