Hi GT5000,
If the goods are being shipped from your factory in the EU to consumers in the EU then this will be Outside The Scope of UK VAT as the goods are never in the UK.
However there will be a supply within the EU on which VAT would need to be charged.
If you own the goods in one member state and sell them to a consumer in another member state then this will be classed as a distance sale
There is a One Stop Shop System within the EU which allows you to account for a VAT in a single member state rather than having to register in all the member states where you make supplies to. Please see the guidance below:
VAT on e-Commerce - One Stop Shop
Thank you.