When marrying a Foreigner (meaning one has another Citizenship than yours), each Citizen have to follow the marriage laws and rules of his/her Citizenship country (and if residing abroad of both Citizenship Country, the marriage laws and rules of the living Country).
So it can be a bit complicate!
If not living in the Citizenship country, it's your personal choice if you don't want to follow your Citizenship country laws and rules. You should not have any difficulties if you do not go back to your Citizenship Country (except if you need some paperwork linked to this marriage). But if you do you may encounter some small or big difficulties (I don't see any Filipina not coming back to the Philippines from time to time, like you will surely visit Italy from time to time!).
If your case she's in UK with a Student visa and can't file a divorce there as not a resident. So she have to go back to the Philippines.She can surely file and get a divorce in Guam or Las Vegas but will have to travel there. In both case, she will need a US tourist visa (B-1 visa) and as tourist visa it's hard to get for a Filipina (hard but not impossible, just know that 90% are rejected).
So I think, even if I perfertly understand it's a long and difficult process, that the best way for both of you is her to file in court an annulment procedure in the Philippines.
In the middle you can try to request a tourist visa for UK. It's like playing lotto: you pay first and then a few win, most lost.
