I read your first sentence and I was all “Tell me where you need me, Bingley,” and then I realized you meant something else.

Brexit. Brits left the EU and threw out a great deal of the foreign work force. Not realizing that this same work force do all the loww paid jobs that keep the country running. Like driving the trucks. UK is now lacking some 100 000 drivers. No wonder delivries do not funktion as it should.

Apparently SE of England is having petrol shortages.

Hardly surprising as most of the supply comes into the UK via either the north, or Milford Haven port in west Wales.

Haven't seen video clips of people filling garbage bags yet though.

It seems like it is not a petrol shortage per se. It seems like it is a distribution problem due to a lack of truck drivers. They have the petrol and just cannot get it to the pumps. Apparently there are plans to use drivers from the military to relief that problem.
Some pubs also have a distribution problem with beer. The commonwealth citizen Slim Dusty performed a song about that: https://www.youtube.com/watch?v=7cKPchRDaVM . As a funny coincindence rumor has it that the reason was a transportation failure as well: https://www.youtube.com/watch?v=KkDUBYOzyAQ
Got to love the Aussies for creating fitting songs decades ago.

Actually beer shortage probably due to lack of carbon dioxide. Also used in packing meat products and so on.
Again as you say, probably down to distribution.

Think a lot of people in gov didn't think Brexit was going to really happen and even after the vote believed someway somehow it was going to get reversed, and never really put any planning in place for the eventuality.

Our local COSTCO last week was out of Mexican Coke (made with sugar, not corn syrup) and also out of Charmin, my wife's preferred TP. So, today we stopped at another Costco on the way home from a meeting. They had the Coke, but had NO, Nada, ZERO TP at all. Other paper products were available, but no TP.

The supply chain issues are happening everywhere due to truck driver shortages. Not many people want to / can live the life, its a long lonely and boring life and you have to put up with the stupid (car) drivers and the company wanting you to get there faster and having to worry about the log books and laws around them. So companies can't find drivers and the old drivers are overworked and getting sick and tired and quitting/retiring.

For those who are out of TP...

Consider buying a Japanese toilet instead. Think about it: if you stepped on some doggie doo, would you just wipe it off before walking all over your carpet? No, you'd wash it. The same logic applies to your toilet. You can just install a seat that hooks up to a water source.

Or install a bidet shower next to the toilet seat.
https://upload.wikimedia.org/wikipedia/commons/thumb/d/db/Bidet_shower.jpg/1200px-Bidet_shower.jpg