I have two 7 year old twins, their mom died only a few months after their birth so I raised them on my own until they were about two years old, then I met my now ex-girlfriend with whom I had a relationship for three years. The kids call her mom and she loves them like her own. We've been "sharing custody" I may say, since it's not legally, for the past two years. We've been worrying for some time now that if ever there was any problem whether it's medical or legal issues, she won't be able to get involve since legally she is no one to the kids. That's why we've been wondering if there was any way that she could adopt the twins and become officially their mom.

Depends on your general locale. Some areas require that partners be married to allow for such an adoption.

I live in New York and to make it even more complicated my ex-girlfriend is British.

1. Who can be an adoptive parent?  An adult over 18 years of age, whether married or single
 An adult married person legally separated or not legally separated and living apart
From their spouse for 3 years
 Same sex partners may both adopt a child
 An unmarried partner of a child's birth parent
http://iaatp.com/docs/faqs-ny.pdf