A Divorce petition initiated by a Filipino citizen is not valid in the Republic of Philippines, the Philippine Family code does not recognize a foreign divorce, a Filipino citizen must inititate an anulment proceeding should they wish to dissolve a marriage they have contracted.
The only time a Filipino may have a marriage dissolved in the United Kingdom is if they have become a naturalized British Citizen, however, even if the marriage was dissolved through the British courts, (and you dont say if the Filipino is male or female) I am assuming the divorcee is a Filipina, if the divorce petition was initiated by a Filipina in UK, and she was married to a Filipino, it would not be valid in the RP, if the marriage was to a British Citizen, it would be valid in UK, but not in the Republic of Philippines, since at the time of the divorce petition, the Filipina is subject to the laws of the RP.
If the Filipina attempts to obtain entry clearance for the United Kingdom, that would tell me, that this person is either here on a tourist visa, a work permit, and or is undocumented, if undocumented, its highly unlikely that this person will be granted an entry clearance visa, as they will need to explain there absences from the RP, and also, there overstaying, secondly, if on a work permit, they would still legally be married as a Filipino Citizen, the only authority the Philippine Government will allow to dissolve the marriage of a Filipino citizen is their own, that is the Philippine courts.
I hope that helps.