If the credit card is in your son's name then you have absolutely no liability and they cannot demand payments from you.
Peter is wrong about the information the credit card companies have. His account is his account. Nothing to do with you.
There *may* be a link to your son on your own credit history as recorded by the credit reference agencies, particularly if you have ever had any joint accounts. This is more about how easy it is for you to get future credit than being chased for old debts. It could make it more difficult for you to borrow in the future if he ever defaults on his CC. Just having a debt is not really a problem, missing payments on it is.
If you are financially separate (ie no joint accounts) then you can ask the credit reference agencies to sever the link between you and your son. Then his history will not appear on your reports at all.
http://www.experian.co.uk/consumer/faq/AR3.html