Lived and worked in Thailand where they produced labels saying Made in France, Made in almost anywhere - and, of course, we have no control over anything put into the product. If supermarkets ask us to pay more will they reform and buy British - nope - already there are 'ways around' labelling imported allsorts - will they just pocket the difference - yup. The only way to be sure of what you are eating is buy it yourself locally, and cook it, wrap it, spread it, yourself.
An-other tale - a major supermarket ran out of 'welsh lamb' - their policy was to load lorries with lamb, drive it over the border into Wales, let the driver sleep over, and the consignment gets re-labelled the next day as Welsh Lamb. And I truly had that from the horse's [hah] mouth.