I don't believe you need worry about your baby having a UK passport as regards leaving or entering.
From what I can remember there is no visa requirement for children under 2 years...entering staying in or leaving the Phils, but you may like to check on the Phils govt site . No problems for the baby entering the UK of course.

My own child was in this situation more than once, but a few years ago

Mother, as a Filipino will need to pay Travel Tax (last I heard it was 1,620 pesos)+ airport tax of course, which I believe has been put back down to 550 pesos now, but more recent travellers than me can confirm. (All this type of information is available on google search of course).


A good idea to get a chest Xray done for your wife only...and keep it to show UK immigration if asked.