The practical benefit of British citzenship is that you can travel without a visa to many more countries with a British passport than you can with a Philippines passport, and you can work anywhere in the EU without a work permit.

Remember that the UK permits dual citizenship - the British Government does not require you to give up your Filipino nationality as a condition of gaining British nationality

An awful lot of Filipinos do hold dual citizenship.

So there is really no downside to holding both citizenships.