What courier company is it? Normally the courier companies such as UPS or DHL deal with the customs and if there is import duty to be paid then they hold onto it until you pay. And if you do not pay quickly they will start charging a storage fee. Basically ring them up with your tracking number and pay the fees over the phone.
If it is normal mail and being delivered by royal mail, then it will go to your local royal mail depot and then your postman will deliver a card through your door saying how much the duty is and then you go collect the package from the depot and pay them the money.
By the way, never buy a branded product from overseas (especially China) as it will be fake. And if you buy cosmetic/make up items from outside the EU it is up to you to test them and ensure they are safe for customers. I buy false eyelashes which come with glue from china. The glue goes straight in the bin, and I buy glue from the UK to sell seperately.
Hope this helps.
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