Comparing the back of your watch to other RN issued Seamaster 300s, it appears pretty clear that the case has been milled down at some point.
Even if the watch was not issued (and didn't get the deeply engraved issue numbers), the factory engravings are long gone, along with any of the factory finishes.
Equally, if it had been worn on a NATO strap for any period of time, you would expect wear marks (I've yet to see an issued SM300 or CWC without them)... which are gone.
TL : DR - for whatever reason, as some point the base back has been milled/polished. If you want to know for sure whether it's a legit Royal Navy Seamaster 300, you're going to need an extract of the archives. Bear in mind, that even if the extract states that this watch was sold to the MOD/Royal Navy, the lack of marking will put a lot of military collectors off, and will substantially affect the price they are willing to pay should you ever sell.