hello expatkid welcome here
you have to register the birth of your baby to the british embassy check the link here for procedures and forms:
http://ukinthephilippines.fco.gov.uk...register-birth
after the registration you can get your baby a british passport and won't need a visa to go to the uk..your baby is a british citizen by descent as she is born outside the uk with a father who is (as u said) a british national.