On initial issue of my EASA SPL I had the TMG extension included - on the basis that I already held a TMG rating on my CPL.
Based on that I would have thought that the CAA would add the extension, to your SPL, or LAPL(S), based on the fact you now have a TMG rating on your PPL - of course, you will have to cross their palms with silver.
Just my thoughts - I'd give them a call.
OC619