What bothers me slightly is frogshopUK is based in the US. Still, I bought through Amazon.co.uk, didn't I?
Edit. Buying the same item from the same seller through Amazon Marketplace brings the price down to £175 but I didn't choose this because I knew I would have to pay VAT + duty.
Your invoice is tax free as you are still (indirectly) paying someone in the USA and we don't have to pay their taxes.
Hope this helps.
It's just like buying from them an 'Indigo Starfish' supplying the goods from Jersey, you don't get charged VAT and there's nothing for HMRC to reclaim from you as you aren't the importer.
The price in the link has gone up from £208 to £225. Wierd.