Taken from Google
If you are dropshipping from outside of the EU into the UK, then the place of supply is considered to be where the goods are shipped from, rather than where they arrive. In this case, as the place of supply is outside of the EU, this means VAT is not due on the sale of the goods.
1. If your product is below 135 GBP let's say 100 GBP:
You need to charge 20% VAT at checkout so 100 + 20 = 120 GBP that your UK customer pays to you at checkout. You also need to register for a VAT number in the UK and receive a UK VAT number. The item is shipped you are the importer. The package stops in customs. They see here is a product sold for 100 + 20 was already paid in VAT so you do not have to pay any additional import VAT. You clear UK customs: pay duty (cost to you) and show them your UK VAT registration number. You file to the UK tax authorities and pay them the 20 GBP you collected in VAT. Your profit is 100 GBP minus duty. Customer paid 120 total.
Freight forwarders are looking into ways to offer this service but have not figured it out yet.
2. If your product is above 135 GBP let's say 200 GBP:
you can certainly do things the same way as above (40 in VAT clear customs duty UK VAT # file to UK and pay 40 to UK tax authorities).
make your UK customer pay the import fees to the mail office or shipping company. Meaning you charge only 200 and no VAT (0 in VAT). You ship the product clearly marking that your customer is the importer (the shipping doc details important). The package stops in customs and the shipping company/broker clears customs and pays the duty and VAT to customs . The shipping company then hopefully can collect the VAT and duty from the private customer in the UK. If you use the postal mail, they will charge on the import fees to the customer before they release the package, just as they do today.
Does that make more sense hope? As you can see this is very simplified answer and certainly does not apply to every situation. Please let me know if you have any follow up questions.
P.s. my answer above is if your selling to private customers in the UK
B2B you should make the your company client the importer of record.