Dave,
Stay on the high ground and get an EASA PPL with both SEP and TMG Class ratings. It will cost a little more but once done you can keep both SEP and TMG privileges simply by flying the TMG. You will not be able to add the SEP to a LAPL (S) and will probably cost you more in the long run.
One question re the original UK PPL, was it Group A and SLMG or a PPL (SLMG)? I have assumed the former. All you need to do is a Class rating test in a SEP where you demonstrate the use of Nav Aids on the same flight.