BNO & FCO in London
According to the FCO there are about 3.4 million holders of BNO passports in Hong Kong alone. This status was created by the Hong Kong Act of 1985. This which was to allow BNO passport holders the same status for travel as British nationals. This was done during 1987 and 1997 and nobody was allowed to apply after that date. Likewise the status cannot be inherited. So only the passport holder and not their children would had not applied would hold BNO status.
Likewise note however that the BNO status renewal does not give the holder the right of abode. This in either the UK or Hong Kong, nor are BNO holders considered UK nationals by the EU. The status only allows BNO holders the right to UK consular assistance. This and protection however not in Hong Kong, Macao or China. As China does not consider or recognise dual-nationality China. They considers BNO holders to be Chinese citizens.
There has been a lobby for the British government. This to view and to consider asking countries to treat BNO passport holders like UK citizens. This for visa and immigration purposes. You can see the listed of visa free BNO countries on here. However you need to email the Embassy in that country to ask if they still view BNO as British. British citizenship for a BNO holder at present is only on the bases of ‘stateless’ people. Mainly for those who have not revoked their current or older citizenship status of a country. This has been explained under BNO to British citizenship.
Currently under discussion at this time, to allow BNO passport holders to travel visa-free in the Schengen area.
Additionally with regards to the BNO & FCO in London, you can download the full report here