If born in the UK your baby will be British...as previously stated.
You can then apply to the Philippines govt. for what is known as 'Recognition' (meaning the child is also recognised as being a Filipino citizen, on account of you being born Filipina).
That is what I did after my son was born.
We have never actully applied for a Filipino passport for him (He has a UK one), but is permitted to stay for unlimited periods of time in the Phils without needing a visa.
