Register the child with the British Embassy first.
Obviously the father's name must be on the birth certificate. He MUST be a British Citizen with a British passport.
If you want your child to primarily be a British passport holder (best of course), you can at any time also procure what is known as 'recognition' as a Filipino citizen too. You will be given a certificate for this from the Phils authorities, and then your child can stay for unlimited periods in the Phils without a visa, but still have a British passport.....no Phils passport required.
I did this for my son, although he was born in England.
It effectively gives dual citizenship without the need for 2 passports, or being restricted for travel.
I don't think the Phils allow 'proper' dual citizenship anyway.
