Hi,
If you are selling goods over a value of £135 to UK customers and you are the importer of record then you are the deemed owner of the goods in the UK and so you would account for the import VAT and then charge and account for VAT on the onward supply of the goods in the UK. This would be a separate VAT invoice raised and would not be included on the commercial invoice.
Import VAT however should not be charged twice to both you and your customer. If you are charged import VAT then you have an entitelment to recover this as input tax if you are registered for VAT in the UK
You can see the creiteria here:
Introduction to input tax
Check how to get your import VAT certificate (C79)
We would advise you to speak to the shipping company about the regulations concerning who would need to be the importer of record in the UK and also speak to our International Trade Team about this.
Imports and exports: general enquiries
As the importer of record it is the responsibility of the importer to account for the VAT and then to account for the onward sales VAT in the UK.
Thank you.