There is a big difference between leaving a foreign object in someone's vein for several days as well as putting medication through it, and having a simple blood test. If the doctors did not find any other underlying reason for why you had this thrombosis then the risk of a further one after a blood test is very small. And if it did happen again would suggest something more important is going on which would affect your medical longer term.
The UK CAA state this "Please note: The UK CAA has been advised by the German Authority (LBA) that, due to German national law concerning Data Protection, the LBA are unable to facilitate the transfer of pilot medical records from Germany to other States. It is therefore not possible to proceed with transfers of State of Licence Issue from Germany (LBA) to the UK (UK CAA), or indeed any other state, as the whole certificatory medical record of pilots must be held by the state to which a licence is transferred. Please note that German pilots’ licences are fully valid in all EASA member states." on their website taken from here
https://www.caa.co.uk/Commercial-ind...te-or-licence/
So unfortunately change SOLI may not be possible either in this situation.