C0 would have made sense, though I don't remember seeing it anywhere.Would they not maybe have used the C0 code for these regardless? Unless it was specifically introduced for them after introduction as DEMUs.
I can't remember whether SR emus carried restrictions at all (anyone?), while vans had actual dimensions painted on the side.
An intriguing question is - if C0 was totally unrestricted, and C1 virtually* "go anywhere," what if there had been BR hauled stock to SR restriction 1 (Tonbridge to Grove Jn, T Wells - not Eridge as I said earlier, sorry)? It's academic, as the only such stock was the 3D/class 207 units.
* I know there were other restrictions on Other Regions.