Your understanding is correct - the NPPL declaration is signed off by your own GP.
For those who don't meet the HGV standards, there is the alternative of a less demanding standard which will allow you to fly but not to take passengers.
Given the type of flying you do (and assuming that you don't fly anything with more than four seats or heavier than 2,000Kg), you'd be completely unaffected by changing to an NPPL, except that you'd save money on your medicals!