Sorry, these are not necessarily correct statements as also pointed out by Keith.
There are a number of caveats but generally children who are born in the UK on or after 21 May 2002, or in a qualifying territory, will always be British citizens otherwise than by descent if, when the child is born, one of the parents is a British citizen (it does not matter whether the parent is a British citizen by descent or otherwise than by descent).Your child is automatically a filipino citizen, you can apply your child a Philippine passport to Philippine Embassy in London.
We have heard your side but do not know about the other party, your husband's perspective; it's his child too and I hope you won't ignore that fact. Fortunately for you and not so for the child's father, although the Philippines is a signatory to the Hague convention its provisions are limited in this circumstance.
In any event, I hope that you both will be able to set aside your differences and think of the best interests of the child going forward and not any selfish or spiteful agendas either of you may or may not have.
I would also add that you need legal counsel and encourage you to seek advice from the CAB.
I pray for God's wisdom to direct you both.
God bless you all.