Amazon FBA makes it very easy for non-EU sellers to do this and stay hidden
Having traded on Amazon and EBay for many years, I'm certain that they are both complicit in facilitating this with the ease of anonymity for sellers.
The sellers just need to declare a low value on import because the import VAT and duty is much lower than the retail sale VAT.
HMRC could cut out 99% of this method of VAT avoidance by just forcing Amazon and Ebay to publish seller identities, and report back to HRMC sales reports.
No need to chase thousands of dodgers, just make the 3 big companies encouraging it responsible.