@ DS - Your medical should be an IAA one too, it may be issued by a German LBA AME but your medical certificate should state under Licensing State IAA and or Ireland.
If it was indeed done by a German AME they would have sent the paperwork to the IAA as that is your State of Licence Issue (SOLI)
If so you can go onto the UK CAA website and make an application for a SOLI-change.