Can't EU/EEA/CH citizens living in the UK before the end of the transition period apply for settled or pre-settled status depending on how long they've been there? There's no reason they would be forced to leave, if so, although of course some may choose to do so anyways.
I doubt it's career sandwich makers -- people may currently qualify through continuation but are probably doing the job as a short term (eg working through Uni). When they finish the next tranche of workers won't have established residency and so won't qualify for visas.
That aside, if someone is here under freedom of movement that doesn't mean they qualify for a work visa, surely? No low-skill jobs would meet the income threshold needed to get a visa?
I think he means forced to leave because they lost their jobs at Pret/etc, not because of immigration law. In fact he might just mean they'll be gone from those shops.