Re: (amazon) we don't have the authority to review their tax affairs.
...And, presumably, real VAT numbers are held on a database, even if not publicly available...
Errmmm... every single registered VAT registrant in the EU can be checked in seconds on the VIES database run by the EU... and other VAT-registered businesses wanting to safeguard their position can enter their own VAT registration number and obtain a cryptographic "hash" that proves their due diligence in checking. The VIES database is available online for all, pretty much 24x7.
Oh, and by the way, if anyone is interested, without a shadow of a doubt Amazon is complicit in all this because they not only advertise traders' products and ship their (sometimes shoddy) products from UK fulfilment centres, but they also actively hide their identities so that fraudsters can trade completely anonymously. Don't believe me? Check the EU requirements on traders to disclose key information (name, registered office address, registration number, etc., etc.) about their identity [implemented in UK domestic legislation as The Company, Limited Liability Partnership and Business (Names and Trading Disclosures) Regulations 2015, made in accordance with the Companies Act 2006 - see Regulation 25 specifically] and then tell Amazon that the trader isn't complying and won't respond to any messages requiring these details. Amazon's finest call centre gophers will come back to you and tell you that the trader hasn't responded to their attempts to communicate with them either, so there's nothing that can be done!!
I bought a Christmas present from an Amazon supplier but didn't get a VAT receipt, in fact I got no receipt whatsoever, and I have no idea from whom I bought it - the name given on the Amazon site is a company that ceased trading over two years ago and whoever is behind the operation hasn't responded to any requests for their identity. So I have no consumer rights and can do nothing should the goods fail in any way whatsoever. And although Amazon processed the credit card transaction for the anonymous fraudster, sent the goods on behalf of same, and isn't offering their (worthless) "A to z Guarantee" for this purchase, it's "nothing to do with them"...! Well, not until you pass full details to your credit card company for a purchase over £100 and request a full refund courtesy of Section 75 Consumer Credit Act 1974, it isn't. When Amazon starts squawking and asking for the goods back after I get the refund (or have to recover it from the credit card company in the County Court using Part 27 proceedings), my intended action is to tell Amazon "please see your e-mail confirming that it's nothing to do with you" and blank them thereafter...