I can not be sure when the British first arrived in the Philippines, the first reference I can find to the British being in the Philippines is about 1686–1688.
William Dampier who was an English navigator and explorer who is most well-known for being the Englishman to explore parts of Australia, he was also the first person to circumnavigate the world three times, was in the Philippines between 1686–1688.
Dampier arrived back in the UK in 1691 with a tattooed slave from Mindanao
He had brought home with him from Mindanao a tattooed slave, whom he called the “Painted Prince Jeoey.” So Painted Prince Jeoey was probably the first Filipino to step foot in the UK. He was exhibited as the first painted savage ever seen in England.
However, William Dampier is not someone to be admired as he was later court-martialed for cruelty.
Jacques Nicolas Bellin a French hydrographer and geographer made a map on a copper plate in 1757 of the Philippines Islands.
It is a Strange map and is based on information gathered by Dampier. If you look close you will see numbers engraved between the islands this represents how many days it took the local natives to sail between the islands.
On the far left of the map, you can see Mindanao. We know today that most of the Islands are to the North and Northwest of Mindanao, so for us, it seems the map is incorrect. But it presumed the map was more about travel time than it was about the longitude and latitude positions of the Islands.
If you know of the British arriving before William Dampier please let us know.