Though if British people stopped eating imported figs, the volunteer fig trees would eventually cease to appear, because British fig trees do not produce viable seed. This is because we do not have suitable insects to pollinate them, which is a very specialist task because of the very curious nature of the enclosed fig flower.

All sorts of plants will self seed in the vicinity of one you planted, but it doesn't mean that they will in general self-propagate in the wild. For example, several volunteer achocha (Cyclanthera pedata, an easily grown and tasty curcurbit, also known as caigua) appeared in the vicinity of the ones I grew last year. But in the ground they didn't germinate until about late May or early June, which was too late in the season to get them sufficiently advanced to fruit and give viable seed. You need to plant them indoors in April to achieve that.