Not exactly, Thomann (poor example) will have exceeded the distance selling threshold and are VAT registered in the UK I suspect. VAT is charged according to the place of supply rules and is where the supplier is established, unless selling to a taxable person in the country of destination.
Either way, you are definitely only charged VAT once. Duty rates can be around the 4-5% mark and VAT is calculated on the value of the goods, the Duty and transport costs so the goods will be more expensive (depending on the rate).