I would say go to Greenwich as your parents are telling the truth, and I can tell that you know it too. But only you can make that decision. Although this sounds harsh, you're going to have to be ready to face what comes with leaving home if you go to Huddersfield (i.e if you can't get a job/homesickness etc). I had friends that spent more time travelling back home every weekend for food, or worse still, asking housemates if they could have some of their food, because they didn't have money; though most of that was their fault, but I'm trying to paint a picture of how hard it could potentially be.
I'm travelling away from home for uni, only because my parents are willing to support me and I have close family friends nearby where I'll be going, so I can always fall back on them for food or company if I don't make friends or I'm bored. Sorry you feel this way though, I know it must hurt. You never know you might actually like Greenwich, and there must be activities that you can get involved in to meet new ppl, because London is a big city. I can't give you advice on your parent, other than you must be 17-18, so you're grown and your mother can'y baby you or smother you forever. Good luck.