It appears that I misunderstood the process of BN(O) passport holders getting British Citizenship by serving in the British Armed Forces. After reading a House of Commons debate in 2013, in which the then Immigration Minister stated that -
Foreign and Commonwealth personnel in Her Majesty’s armed forces are exempt from immigration while they are serving, which means they automatically meet the requirement to be in the UK without a time limit attached to their stay. ...
Therefore, foreign and Commonwealth personnel in the forces are eligible to naturalise as British citizens after they have served for five years. Alternatively, under the immigration rules, they might qualify for settlement—indefinite leave to remain—on discharge, after four years’ service. They cannot obtain settlement in service because someone who holds indefinite leave to remain is subject to immigration control. If the person opts to be discharged and settles in the UK after four years’ service, they can apply to naturalise after they have held ILTR for one year, thus fulfilling the five-year residence requirement and the requirement not to have a time limit attached to their stay.
(HC Deb 13 Sept 2013 cols 1319-20)
https://publications.parliament.uk/pa/cm201314/cmhansrd/cm130913/debtext/130913-0001.htm
A layman's understanding of the UK Immigration Minister's speech in the House of Commons noted above suggests that current Commonwealth members of the British Armed Forces with at lease 5 years' of service can apply for British Citizenship without the need to get Indefinite Leave to Remain (ILR) [永久居留] first.
On the other hand, those Commonwealth Citizen who left the British Armed Forces with at lease 4 years can apply for ILR.
You cannot apply for ILR as a serving member of the British Armed Forces. This is because serving members of the British Armed Forces are exempted from immigration control in the UK, however ILR holders are still subject to immigration control in the UK.