Firstly you will already know that there's nothing you can do or say to have the passport office change their policy.

To renew the Philippine passport to show married name will take between 12-18 weeks.
The Philippine Embassy no longer do name changes as they did years ago and now send to Manila for a new one.
This would need to be done before any application for British Passport but the naturalisation ceremony can still take place as long as you do not inform the Philippine Embassy. Technically the Philippine citizenship and eligibility for Philippine passport no longer exists.

To get a new passport in married name you'll need to provide the marriage certificate and certified copies. Depending which country the marriage was made will determine where the certified copies need to be done.
Another complication is whether or not a UK marriage was reported to the Philippine Embassy on time. This would need to be done if not done already.

The only alternative option is to have the current Philippine passport cancelled due to no longer being a Philippine citizen. Technically this should be done after Naturalisation as a British Citizen.