As promised herewith my correspondence with HMRC about this. I asked if there was any sort of agreement between HMRC and eBay in the USA or the USA Government about these so called "pre-payment" facilities where a UK buyer pays money to the US seller.
And the reply:
Thank you for your query of 30th April regarding imports from the USA. As you correctly point out, the USA is not party to the agreement. Consequently, my advice is that you do not take up this supplier's offer as it will only lead to you paying Customs charges twice. Instead, you should pay, via the carrier, only when the parcel arrives in the UK.
Robert White HM Revenue & Customs