Terminology, PPL (SSEA). The SSEA is only applicable to a NPPL so can be added to the existing NPPL in accordance with CAP 804 Part II Section 5 Appendix 1.
The only problem is that the NPPL(SSEA) is not valid on an EASA aircraft and the licence can no longer be converted to an EASA PPL
An alternative other option would be to do a LAPL and then upgrade it, or as you say do the full PPL course.