No worries! I got given the runaround by NHS Overseas Healthcare Services too initially but S1’s should definitely fall within their remit. It may depend on your NI contributions which is why you should probably need to check with HMRC.
If you get the runaround from NHS Overseas Healthcare Services their complaints email address is firstname.lastname@example.org.
The key thing is that HMRC need to have your up to date address details.