First off, did you live in the UK for the first 10 years of your life? If you did you can apply using Form T which makes it all a lot more simple. More information is on the UKBA site here -
http://www.ukba.homeoffice.gov.uk/briti ... ornintheuk
With British Protected Persons the UKBA accept this is confusing and recommend you to call them if you've got questions. To have a stab at it for them though... As you father didn't get his passport through desecent (called 'otherwise than by descent') then he can pass his citizenship on to you. The following, taken from the UKBA page 'Am I a British protected person?' should help clarify.
"From 1 January 1983, the following categories of people became, or were able to become, British protected persons:
* anyone who would otherwise be born stateless, on or after 1 January 1983, in the United Kingdom or an overseas territory if, at the time of their birth, their mother or father was a British protected person.
In most cases, British protected persons lost that status when they gained any other nationality or citizenship, including British citizenship, British overseas territories citizenship or British Overseas citizenship."
What this means is that if you were born stateless in the UK then you would be a British Protected Person, and eligible to apply for citizenship. However, if you subsequently became a citizen of another country you lost that staus, and the associated right to apply for naturalisation.
If your father only achieved ILR/citizenship after you turned 18 then you can't apply as his child either, as you are now classed as an independent adult. This means you will need to apply through the normal channels -
http://www.ukba.homeoffice.gov.uk/briti ... igibility/.
Hope this helps.