Do they have to? You've already admitted they are your debts. Who knows what proof they have, or how they found you. when they take you to court, you wont be able to prove it's not you, so will still have the consequences.
Did you know its against the law not to register as living where you do when the council send you stuff round? Dont you pay council tax?
perhaps i may suggest a way out of this situation? Pay your debts, then they wont be able to send round the debt collectors because you wont have any debts. Next thing will be baliffs coming to the door and takig your things against the value of the debt, or court summonses, or ccj's in your absence, making it very difficult for you to get credit in the future.
there is always some sort of trail, as you have found out