I am afraid there is no way of clearing your name. You should get a copy of your credit files from experian and/or equifax. Check that all the arrears/judgements are shown as satisfied. If not, contact the companies and make sure they ammend their records.
These details will remain on your files for 6 years and there is no way of getting round it I am afraid without changing your name and moving - even then if you do not give a previous name/address when asked you would be committing fraud.
Although main lenders will not give you credit if your history is chequered, most car dealers will have a secondary company who will consider you (especially if you go in with a sensible deposit - around 20% would be good) - I know as I work in this market