As long as the parent living in the UK has a legal right to remain here (ie. a legal immigration status) then it should not be a problem obtaining a visa, but they will have to get one before they travel.
They will have to apply to the British Embassy in the Philippines or they can attempt to do so online on the link at the bottom of the page.
You will see that the the requirements are slightly different depending on whether they are traveling with an adult or not (see "Special Visitors: child visitors). A small fee is payable, I believe this to be around £60 per visa application. They applications are aimed to be completed no later than two months but it depends on how busy the UKBA are and these can even run to three months or as little as two weeks - it's a bit of a lottery I'm afraid.
Here is the link to all the information you need to apply:-
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