Notwithstanding any action taken that may by HMRC, if you have been charged VAT by a business that is not vat registered then if the business refused to make a repayment you could claim the overpayment through the small claims court. I cannot think of any valid defence to charging vat when not registered.
With regards to Amazon/Ebay suppliers not providing (vat) invoices, I suggest emailing them and advising them that unless they comply with your request for an invoice you will report them to HMRC. Sending an invoice is not optional.
HMRC is going after businesses operating through Ebay, Amazon or via an internet shop that may have not registered as a business or who may not be declaring all income.
Whereas I am in favour of competition, it is impossible for legitimate businesses to compete against those that do not pay tax or account for vat properly. They can have no complaint if they are shopped to HMRC who do react to complaints of malpractice.