Upvote:3
Yes, you can. See Transfer your visa to a new passport:
You donβt have to transfer your visa - you can carry both your old and new passports when travelling to or from the UK instead.
Note: while they're not explicit about this, a typical rule is that this only works IF you did not change your name or citizenship.
The airlines know that, but Philippine passport control might not (and try to avoid flying out of Manila, where the passport control seem to give the most hassle to Filipinos). Carry a printout from this site with you.