Will it be a civil wedding or Catholic Church wedding?
In addition to the info and links posted by lastlid. here is some other useful general information about overseas marriages and civil partnerships
and some CNI information here including the British Embassy appointment system and how to apply
CNI information here
Please do remember the CNI has only 3 months validity, so plan out carefully what needs to be done and when. It's a good idea to make a project plan from wedding day backwards so you can line it all up.
The CNI is available from your local registry office. It takes 22 days from time of application. It's 21 days for the 'bans'.
You'll need to pre-book an appointment at the British Embassy in the Philippines to be issued a Philippine version called a Certificate of Legal Capacity to Marry.
This certificate is needed for the application of a marriage license.
Yes, many people are now reporting that you may well be required to obtain a your own CENOMAR (Certificate of No Marriage) from NSO (National Statistics Office) so you might need to include this contingency as well.
I suggest you always check the latest information for paperwork needed before leaving UK