As said above, the company/requestor are usually the only type of people that can remove these marks. How long ago are we talking here?
As for CCJ's , they are only court issued...hence County Court Judgement. Were you never contacted about any outstanding debt / bills etc? It does take a LONG time for these type of things to come around. Did you move house without forwarding addresses etc?
Also as above, firstly contact the company. See what they have to say and how much / what you owe them. Also when they cancelled your contract. Remember the calls are recorded. If they aren't really helping ask for all the data held on your record to be sent to you (usually a charge) but they have to do this by law on your request.
Secondly, go have a word with your local citizens advice bureau. Take all appropriate documents and PROOF that you cancelled your contract by letter, though that usually involves a receipt which most people don't keep.
Thirdly, depending on what company it is, have a word with Financial Odbudsman Service (depends if they are governed by them) See what they have to say and if they can help.
Hope it helps.