At the age of 16 (in the UK) you have the right to walk out of your home and never have any contact with your parents again. (If your parents reported you as missing, and the police located you, the police would be prohibited from revealing your whereabouts to your parents).
So you certainly have the right to leave home. Once you leave home it's entirely up to you to decide where you'll live. That's the legal position but, of course, 'family politics' are often just as important as the law. If you want to live with your sister, and she's happy for you to stay with her, nobody has any legal right to stop you (unless your sister is renting the property and her rental agreement prevents her from letting you live there) but that doesn't prevent your parents from putting your sister under pressure to refuse to allow you to live with her.
I note that you've written that 'they' have a spare room. If that means that your sister is living with a partner, he might well not want you to move in.
To summarise: Nobody (other than, possibly, your sister's landlord) can legally prevent you from living with your sister. But 'emotional pressures' might still dictate otherwise.
Chris