For future people:
I called CAA medical: +44 1293 567171
And a nice gentleman explained that the SOLI process is only for holders of a medical or licence from another EASA member state.
In my instance neither FAA or GCAA are EASA so they basically don't exist in the eyes of the CAA and I will simply book an appointment for an initial class 1 medical the next time i'm in the UK.