For a start, you ARE looking at a maze of laws, both US and UK. Disclaimer- I am not a lawyer, but am a gun collector, and know a bit of this. However, legal advice I give you is worth every penny you are paying me for it-
First, under US law, the receiver (frame) of a gun IS the gun. To be engaged in the business here of selling complete guns OR receivers, you must be licensed as a Dealer by the US govt. So your dropshipper in the US would need to be a Dealer, and ship TO a Dealer in the buyer's home state- IF the dropshipper is in the US.
If your shipper is NOT in the US, a license is required here by the IMPORTER of firearms. You cannot ship directly to a dealer OR purchaser from outside the US unless they have that license. Imported firearms may be stamp marked with the name and address of the importer, and caliber. Got provisions for THAT?
Now that we have the legalities out of the way, let's talk practicality.
If I buy a gun from you, I will have to pay shipping, and pay a fee to the Dealer that receives it. When added to the cost of the gun, would the transaction be economical?
Next, not having come to know and love you for the truly wonderful human being that you are, if I were not satisfied with the transaction- what is my recourse? If I send you money, what guarantee that I get what I ordered?
Next, do you have a drop shipping firm that knows the assorted US firearm laws- and knows that a Model X cannot be sold to a resident of Maryland, but that a model Y can?
Now, I DO purchase firearms from US sellers in other areas, my decision based on photos, description, and THE RECORD OF THE SELLER. Different auction sites list the feedback record of the sellers- If 165 other people left you positive feedback for sales to them, odds are you will treat me right. What would you have that is the electronic equivalent of your reputation?
And last- what do you have to sell that I cannot buy from a US firm now? Not meant to be insulting, but a serious question.