This answer assumes that you're in the UK:
At the age of 16 years you can leave home and, if you so choose, have absolutely nothing to do with your family. If, for example, you simply 'went missing' and your parents reported your absence to the police, the police would not be allowed to reveal your whereabouts to your parents. So,of course, you can move out and and live where you like, and with whom you like.
That's the 'legal' answer. I'm certainly not recommending that you should break off all relations with your parents. You clearly understand how strong an emotion love can be. Try to remember that your parents are concerns are fuelled by their love for you. (Yes, I know that it doesn't seem like that when you're in the middle of a blazing row with them, but I can assure you that a parent's love for their child is just as strong as the love you feel for your boyfriend).
Chris