The complicating factor is that Chinese law automatically considers people of Chinese descent living in Hong Kong as Chinese citizens. Hence, BNOs of Chinese descent can not register under any section of British law that requires you to hold no other nationality.
So, it comes down to your ethnicity. If you are of Chinese descent, the route you were exploring is not for you. On the other hand, there has been some success reported on these forums of BNOs of non-Chinese ethnicity successfully registering under Section 4B.
BRITISH NATIONALITY (HONG KONG) ACT 1997 - EVIDENCE TO BE SUPPLIED wrote:
4.8 Applicants of Chinese origin
4.8.1 If applicants produce Hong Kong Permanent Identity Cards which have the symbol ***, it is almost certain that they are of Chinese ancestry and are Chinese citizens (despite the official disclaimer in Annex E). They should therefore be asked, regardless of where they are applying, to contact the Hong Kong Special Administrative Region Immigration Department for confirmation that they were not Chinese citizens.
4.8.2 However, it should be noted that the issuing authority can remove these asterisks at the holder’s request and, therefore, their absence is not conclusive proof that the holder was not a Chinese citizen. Where it appears from the application form or other information that applicants are wholly or partly of Chinese ancestry, they should normally be required to obtain confirmation from the Hong Kong Immigration Department that they were not Chinese citizens at "the relevant date".
Also see
Chapter 14 of the Nationality Instructions: registration and naturalisation under legislation other than the British Nationality Act 1981.
The above considerations would also preclude a BNO of Chinese ethnicity from applying under
Section 4B, which also requires the applicant not to hold any other nationality.
You can of course apply under Section 4, as highlighted by
MrSlyFox, but that requires you to have held ILR for a year. As you have been on Tier 4 visas this far, it is unlikely that you will acquire ILR any time soon (to the best of my knowledge, Tier 4 visas are not a pathway to ILR except under 10 years Long Residency).
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.