Hi Rosie, ok. For your nephew, it's likely he will be eligible for a British Passport (as long as your brother was born in the UK). The procedure for this should be fairly simple, with a copy of the Philippine birth certificate and copies of you brothers birth certificate, and completing some paperwork at the British Embassy, this information is all on the Embassy website.
The wife of your brother will be able to apply for another visa, applications are made through a company called VFS on behalf of the Embassy http://www.vfs-uk-ph.com/ . The application will probably need a few explaining letters, and supporting letters from those who will support her whilst they are initially living in the UK.
The difficult part is which visa, she could apply for a long term visit visa, alternatively she may be able to apply for a fiance visa (this is a full immigration visa, but would require marriage at some point in the future). But I think the probable visa would be a family visa. The problem is I don't know for certain, and because of the exceptional cirumstances of the case, it would be well worth contacting the Embassy for advice on this situation.
The alternative advice (please get proper advice from an immigration lawyer first), but if she applies for a visit visa coming to the UK, she may then be able to apply retrosprectively through the courts system to stay under Human Rights acts. I've heard of a similar case, and it's worth checking into, should the Embassy not be helpful.