The question has been asked many times if the holder of a BNO can obtain British citizenship. The answer is yes and now and there is a law which came into effect in 2010 which cleared the issue well enough. This being the Section 4B of the British Nationality Act 1981.
If you are a BNO holder then you can only apply for British Citizenship if:
1. You hold no other Citizenship or Nationality other than the BNO
On condition that:
a) You have not renounced any citizenship that you may have had;
b) You have not voluntary given up any citizenship you might have had;
c) Loss of citizenship though action or inaction since 19 March 2009.
There is however another note about this being that BN(O)s of Chinese ethnic origin are entitled to Chinese nationality and do not qualify. If you hold on to a Nepalese Certificate of Citizenship then you do not qualify either unless you can prove that the certificate was issued in error. The BNO to British citizenship is mainly for BNO holders who are otherwise stateless persons. If you are one of those then you need to download the applications form from UKBA and call 2901 3050 to book an appointment.