I never recommand to be pregnant when applying for a visa as you never know when you will get it and when you will be able to travel.
The problem will surely be the possibility or not of travelling. The airline may request a certificate from their accredited doctor to confirm if she can travel. You can easily understand they don't like to declare an emergency and do a medical diversion during the flight. If she travel before giving birth, get a good travel insurance in case...
If she give birth in the Philippines, the problem will be the baby travel and papers. If I remember well, the Embassy require your appearence for recording of the birth (your Wife can't do it alone) for the baby to have a British citizenship and the British passport request for the baby.