From the Philippine Embassy London website:-

Additional requirements for married women who wish to use surname of spouse in their passports

(Note: The Embassy will no longer process applications for amendment of name in a machine readable passport. Applicants are required to renew the passport instead)
•If married in the Philippines, the original and a photocopy of the marriage certificate (authenticated by the National Statistics Office). A copy of husband’s valid passport or birth certificate.
•If marriage was performed outside the Philippines, (a) the original and four (4) copies of the Marriage Certificate, (b) four (4) duly accomplished Report of Marriage forms (which are available at the Embassy and at the Embassy website), (c) four (4) passport size photos of husband and wife, taken within the last 6 months, (d) four (4) photocopies of the passports of the husband and wife. The Report of Marriage fee is £18. If the marriage had been solemnized for more than a year prior to the filing of Report of Marriage, there is an additional fee of £18 for late registration.
•If marriage was performed outside the United Kingdom, please submit the original and four (4) photocopies of the marriage certificate duly authenticated by the Embassy of the country where marriage was celebrated.
•In case of death of husband, applicant must provide the original and four (4) copies of the death certificate of the late husband.
•In case of divorce or annulment, applicant must provide four (4) photocopies of the divorce or annulment papers. Please note that the applicant may have her name changed to that of her second spouse only if the petitioner of the divorce of the previous marriage is the foreign spouse.