This I don't know... I would say "may be" but have to be confirmed. You will have to inquire (as your Husband to do it, it will be easier).
Find and read the good infos for your case here:
http://www.bia.homeoffice.gov.uk/britishcitizenship/
In particular:
1) Eligibility for Children:
http://www.bia.homeoffice.gov.uk/bri...lity/children/
2) How to apply:
http://www.bia.homeoffice.gov.uk/bri...ship/applying/
3) How to contact them:
http://www.bia.homeoffice.gov.uk/bri...nship/contact/
I have a last question, does the Filipino birth certificate is fully filled and signed, meaning mariage section and Father section fully filled-in?
I don't know what should be done for UK for the bith certificate, but in France apart the classical Philippines red ribon authentication (NSO, Malacaņang and DFA) we need a full authentication by our Embassy in Manila with their stamp and signature on each page (and over these something you don't need: a duty legalized by an court approved translator in French). I hope it's not that complex for you.
I'm surprised that nobody in this forum had the same problem...