lilbasuk,

The CNI is a Certificate of No Impediment (sometimes called Legal Capacity to Marry).

The UK CNI is available from your local registry office. It is issued after your Notice of Marriage is posted and takes 22 days from time of application. It's 21 days for the 'bans'.
You then need to present your UK issued CNI to the British Embassy in the Philippines who will exchange it and issue you with an official Philippine version CNI (Certificate of Legal Capacity to Marry.)
This local Philippine CNI is required by Philippine law in order to secure a marriage license.

So in your case you do not need the Embassy to post Notice of Marriage. That's only for those British Citizens folks who are residing in the Philippines and need to have their Notice of Marriage posted at the British Embassy.

You might want to consider working the dates/deadlines back from your planned wedding date so you can easily see the whole plan 'datewise'
Your UK issued CNI will generally be treated as 3 months validity before having the Philippine version CNI issued.
This Philippine CNI must be presented for Marriage Licence within it's 3 month Validity.
The Marriage Licence has a validity of 120 days.

I suggest you always check the latest information for paperwork needed etc but in principle you need:-

Birth certificate - original
Passport

Philippine CNI (needed for the application of a marriage license.)

BTW many Brits 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.
Your own CENOMAR can be ordered online at a small cost

For the Marriage License - Apply for this in your fiancée's home town at the registry office. (or locality of where marriage will take place)
You might also be requested to attend the "Pre-Marriage Seminar" counselling sessions prior to being allowed to be married. Check and ask when you apply for the marriage license

After you apply for the license there is a mandatory 10 day waiting period while the marriage banns are published

To apply for the Marriage License you should consider having as many of the following documents as you can:-

Your birth certificate
Your passport
Your C.N.I.
Your NSO CENOMAR (if needed, please check well beforehand)
Your Divorce decree asbsolute (if applicable)

Certificate of 'Pre-Marriage Seminar' (if needed, please check well beforehand)

Her N.S.O. birth certificate (This should be fresh from NSO on latest type of security paper. Check)
Her Passport (or other appropriate ID)
Her Barangay clearance (if needed, please check well beforehand)
Her community tax certificate (often called Cedula)
Her postal I.D. Address
Her CENOMAR
Her Parents signed advice form (for under 25 years)
Her Parents I.D.

Hope this helps a little.

Appointments at the British Embassy were recently running at around 2 months 'waiting' time for a slot.
I'd strongly suggest booking a slot as early as possible.