1. After you have registered your son's birth then you can apply a British passport for him.
2. If you want your son to have a Dual Citizen or to be a Filipino Citizen then it is important for you to report his birth to the Philippines Embassy.
3.For British Passport, you can get an application to your local post office or visit this link http://www.ips.gov.uk/passport/index.asp
For Philippine Passport, download an application form from the Philippines Embassy's website http://www.philemb.org.uk/
How many days you are planning to visit the Philippines?