Let's analyse the situation, your company is registered in the EU so is bound by the EU tax rules however the EU company is importing goods directly to the UK and then selling to customers in the UK and abroad. So import and export are from the UK. Perhaps you are better off registering for Vat in the UK as an EU company.
The business model is quite complex but since you aim to close the EU company, its best to get registered for Vat in UK and then once Amazon account is settled you go for closing the EU company.