Hi Paul W
My daughter was born in Phil in 2003 and my name is on her Filipio BC as her dad. At that time myself and her mother were not married. So at that time she did not qualify automatically for British Citizenship much to my suprise! So when I next visited the Phil I paid my application fee and together with her mum (as you have to both be there to sign various papers) we applied for her to be registered as a British Citizen under section 3(1) of the British Nationality Act of 1981 which is given at the "Home Secretaries descretion".
The form that you have to fill in was available on their website so I printed it out and just answered the questions along the line of that I wanted my daughter to have the same opportunities that I had as a child etc etc, and gave it back to the embassy. A few months later we received a letter saying she was granted British citizenship. And we got her British passport with no trouble. As it turned out our subsequent marriage made it all unnecessary but thats another story! So my advice to you is that if your name is on her NSO Filipino birth certificate as her father and that the mother / father relationship on it says "not married" as ours did then go ahead and just apply. I was quoted £2000 from a so called immigration specialist to assist me. I decided that I had nothing to lose by just doing it myself. At least if I failed they would have to tell me why! you might just be suprised at the result.