There's no legal minimum age for a young person to leave home.
In some cases of family breakdown, social services arrange for 15 (or even 14) year olds to move into their own flats. (They do this where the young person is considered responsible enough, when a foster-care arrangement is unavailable or inappropriate and where social services can provide support. All the same, the young person has left home well before the age of 16 and it's perfectly legal).
Your daughter is old enough to marry her boyfriend (although, up until the age of 17 that would require your permission), so she's certainly old enough to live with him.
Chris
PS: I think that you should be congratulated for accepting that things are the way they are, rather than the way you might have wanted them to be. Things will be difficult for your daughter for some time to come; you've wisely recognised that creating a conflict situation won't help your daughter or yourself.