So, your parents want to have a London pad available to them as and when. They are willing to make this pad available to those children still at uni, outside term-times.
To this end, they bought a studio flat and persuaded one of their children to stay in it. Child pays to stay there. If child were not resident, the studio would have to be rented out, and since they are abroad an agent would have to be employed to manage this rental. They would run the risk of a bad tenant; not paying their rent and trashing the place. Even with a good tenant, the agent's fees will be hefty.
So, having a child in situ saves the parents from damage, worry, and agent's fees. They are effectively an unpaid caretaker for their parent's property, paying for the privilege. 
Child has been considering moving for a while; would cost less and be nearer to work, plus it would be their space that siblings and parents would have no claim upon.
Have I understood the situation correctly @strivingtosucceed ?
Your parents are being total cheeky fuckers here. "The reason I live here is that they ... made a big fuss about my siblings and I having a place to stay." Wow. What a whopper. The reason you live there is because your selfish parents manipulated you with their fuss. The real reason you live there is because it suits THEM to have you taking care of their property for nowt. And now they want to screw you even more.
Move out to a set-up better suited to your needs, and let them get on with it. Let them hire an agent and rent it out commercially. Oh, they won't have access then? Tough shit, there are hotels in London I'm sure. And they can provide for your student siblings, not palm off that responsibility onto you.
I cannot believe how selfish they are.