Sounds like an indirect export, see this Notice,
VAT on goods exported from the UK (VAT Notice 703) section 2.9 and 3.4
If the German seller was responsible for shipping the goods to UK, they can zero rate it as a direct export because for the zero rate to be valid the supplier must have proof of export (shipping paperwork from the freight agent).
Where the customer arranges the shipping, this is an indirect export because the supplier does not have any proof of export, for all they know, you could have arranged for DPD to pick up the goods from the German factory and transport them to a customer in Germany and as you are paying for the shipping, the German supplier does not have any proof or paperwork as all of that goes to you.
So because German supplier has no proof of export, they can't zero rate, hence the 19% VAT charge (which you cannot reclaim on a UK VAT return).
Go back to the German supplier and explain this was an indirect export and present them your shipping documents and proof that the goods did indeed end up in the UK, with copies of this paperwork, the German supplier should then be able to satisfy the zero rating conditions and issue a credit note for the 19% VAT.
If doing future transactions like this (arranging your own shipping), it would be good to chat this through with the seller so that everyone is aligned and you get charged foreign VAT upfront and then have it refunded once proof of export is presented.
