To give a bit of context for those who didn't handle this kind of thing by themselves: VAT used to be handled as part of customs check. In practice that meant that if you were selling to UK (or other EU country) from outside customs union, you'd send your shipment as usual and only attach declaration of contents, and the buyer (importer) would pay VAT and necessary customs fees if applicable.
The new regime apparently requires the seller to setup VAT registration in UK, properly process VAT on their side, then transfer it to HMRC (UK tax agency).
This is a HUGE difference and big burden to both exporters and importers. Yes, importers now don't need to handle VAT - but they are still on the hook for customs fees, and now they have to worry not just about "did the other side file customs declaration right", something moderately easy to fix when it goes bad, but have to deal with "we can't import unless the seller effectively set ups half a company in UK"
The EU are adopting the same rules in July, and I'm not sure why we didn't harmonise the introduction date with the EU.
I'm keeping an eye out for the first "person who has lived in the UK blamelessly for more than a decade is deported" story. I'm also wondering how patchily the parcel enforcement is going to apply to aliexpress and friends.
I’m not sure that the customs changes are significant enough to warrant this reaction, and I suspect most companies on this list are just pausing to make sure they don’t have issues in the short term.
The freedom of people movement changes are much more concerning though.