If the petitioner is Philippines citizen, the divorce will not be recognised in the Philippines, and the original marriage remains valid. That would be a very tricky position when returning to Philippines. On a student visa returning home is a given unless the student gets married in say UK and switches to a settlement visa. These days it takes 5 years to reach ILR settlement and a further 1 year for possible naturalisation. For foreign divorce the petitioner should be foreign to be able to regularise paperwork in the Philippines.
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Then former Filipino citizen wife, who is now a British national, can divorce the husband. Thereafter, she can have the said divorce recognized in the Philippines. This is by engaging a counsel in the Philippines to file the petition. There are two petitions to be jointly filed. The petition to correct/cancel the entries in the certificate of marriage and recognition of divorce. The correction/cancellation of entries in the certificate of marriage is necessary as the divorce decree will not be automatically annotated on the certificate of marriage as a notice to the whole world that the parties were already divorce while a petition for recognition of divorce is necessary for the said foreign judgment (divorce decree) to be enforced and recognized in the Philippines. http://duano.com.ph/TellMeAboutPage/recognition-of-divorce-Philippines.html