I have been selling on Amazon for about half a year now. And from what I can tell, they don't really have a way of seeing that you are dropshipping. The bigger issue will be if your drop shipper is quick. If customers feel they didn't receive their package quickly you will get poor feedback and that is where Amazon will frown upon your account.
i use on .de dropshipping very successfull, when the customer orders the product i give the dropshipper the information to deliver the goods, ok, u cant wait the 3-4 days until u have the money, but when its ok that u get your money 3-4 days later then u can have big success
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what are amazon.co.uk like for dropshipping? 
