Upvote:2
To enter the UK without a visa, your son must have a UK passport, or a passport from a country that's allowed visa-free entry to the UK.* If he has a passport from a country that isn't visa-free for the UK, he will need a UK visa.
It would clearly be helpful to this process if you (on his behalf) had established his British citizenship and secured for him a UK passport. If you cannot establish his British nationality, you can re-start your research on the visa issue on this UK government webpage.
*There are some minor exceptions to this statement. For example, a British citizen who has lost his passport overseas can obtain a Travel Authorization document from a UK consulate abroad that will serve in lieu of a passport and permit one-way travel to the UK. Because your son has never had a UK passport, the UK Consulate in the Philipines will not issue him a Travel Authorization.