I have a quick look and assuming I understand it correctly the process is you first have to adopt in the Philippines, then apply for a visa so your niece can enter the UK, then apply for adoption through a UK court, and then if successful the child could register as a British citizen.
http://www.ukvisas.gov.uk/en/howtoap...tedchildren#Q2
How does my adopted child qualify to join me in the UK?
You, or your child, must show that he or she:
- cannot support themselves financially, is not married and is not living independently away from their parents
- is under 18 years of age
- was adopted when both parents lived together abroad or when one or the other parent was settled in the UK
- has the same rights as any other child of the adoptive parents
- was adopted because their birth parents could not care for them and there has been a full and genuine transfer of parental responsibility
- has broken all ties with their birth family, and
- was not adopted just to make it easier to enter the UK.
Unless your wife moves to the Philippines for at least for a short while I guess you may have problems adopting and meeting points 1 and 3. Depending on the reasons for the adoption you may have problems meeting points 5,6 and 7. Understandably the rules seem to be against adopting relatives purely to allow them to come to the UK for education and then obviously work.
If you think you are going to succeed I guess your first job would be to find a decent lawyer in the Philippines to help you with the adoption. That might not be easy!