In a sense yes, but also in a sense no.
There is a global shortage of drivers. The spin this as the “global shortage of drivers” rather than Brexit, it’s the current governments strategy is divert and blame.
There isn’t SUCH a shortage of drivers anywhere else, The EU isn’t reporting shortages in the supermarkets, but we’re about three months into this now, and it’s getting very visible.
It isn’t everywhere. It isn’t every supermarket in an area. It isn’t every day. It isn’t every product. Some things like high bulk, low cost, long life products have disappeared from the shelves. Bottled water, and supermarket own-brand fizzy drinks disappeared about June around my way. Things come and go otherwise. We had no lettuce/mushrooms/carrots other week there. Nothing. They actually had brown lettuce on one shelf, I suspect with busted bags which had made them go off for the desperate. A few weeks ago there was no raw chicken. None. Wine racks go from partly filled on the cheap end, to one or two left. It hits cheaper products more, higher demand.
I’ve witnessed what could be beer supply problems in a number of pubs in various places. Pubs normally with large selections have only one.
Reports are also that blood sample tubes are in short supply, so instructions for NHS doctors to not do unnecessary ones (speculative low allergy for instance).
On the Brexit side, the shelf life of a typical fresh fruit/raw meat pretty much dropped by half around April this year, as the Brexit backlog was hoovered up. Not lorries, but just a noticable effect.
Is it just Brexit? It is a lot. Is it covid? I don’t think so. That was the first diversion, the “pingdemic” where the crappy app barely anyone uses went crazy once restrictions were lifted, because we were having massive amounts of new cases (50K per day). That was a while ago.
I think a thing called IR35 made a difference. The government brought it in on scale in April (delayed since April 20). This makes self-employed people get blanketed assessed as employees and thus pay more tax, which potentially led to 100-200% rise of taxes paid. Making a shit job which paid well into a shit job which paid badly. So I think a lot left then (it’s had an effect on multiple industries, including construction and IT which hasn’t fully adjusted yet to the idea you either have to pay more, or adjust working practices).
I personally don’t think what the government is doing is going to solve a damn thing. They’re just not competent enough to assess it, preferring to deny reality, believe their own lies, and then blame everyone else and repeat. It’s what they’ve done on pretty much everything (our current Covid stats are underestimates, a disease which takes over 28 days to kill a bunch of people don’t count towards deaths, and new cases don’t count if you’ve had it before, the stats are a lot lot worse)…
For the first time since World War 2, there’s now a minister appointed to secure a food supply in the UK. So some admission of guilt seems to be there.
Any vaguely competent opposition would be tearing this lot apart at the moment, but they seem to fail. A campaign of something like “Remember Oranges?” would be memorable and get the point across, but this leader seems to be about as spineless as the last, though with more charisma and far less baggage.
So tldr:
There’s a global shortage of drivers
BUT Brexit has removed a chunk
Covid had some effect about two months ago
IR35 may have removed a chunk
There are definitely shortages across the board
This is going to be permanent