Too much information!! You are using a combination of a military (i.e. BFPO) address and a civilian Royal Mail one (i.e. HMNB/Post Code). Use one or t'other, not both - I'm sure there will be a Mail Noticeboard on board somewhere, which will tell you the correct address to use...
Depending on the courier, they will deliver directly to the ship (if they are permitted access); will deliver to BFPO as a Recorded Delivery item (where you will sign for it from the Ship's Office on board) or to the Dockyard Mail Office (who will retain the item and notify you to collect and sign accordingly).
If you use your BFPO address, the item will be sent to RAF Northolt for despatch via the internal mail distribution system; if you use the civilian "HMNB" address, it will be delivered to the local Mail Office (probably HMS Nelson, next to the Gym).
If the courier is not permitted access to HMNB, they - or MGS - may inform you when they are at the Main Gate, but they will not hang around as they have a tight delivery schedule. They may allow MGS to retain the item on your behalf, but it is likely that the courier will return the item to the depot for you to make alternative arrangements.
Either way, I would advise that you contact the courier directly and explain the situation to them.