Don't know how you delete your account but your credit card details are not on display. It is a secure site which means during an all information sent to play.com during a transaction, is encrypted and protected against disclosure to third parties. And if you check your account only the last 6 digits can be seen.
If you're still not convinced give them a ring on 0845 800 1020 to see what they can do (but if you're that worried you might want to start paying cash for everything - every single time you pay for something using your debit or credit card you leave a paper trail of your details through receipts, reports, back-ups of transactions, etc. Systems & procedures are put in place to stop staff & others using this information fraudulently but its just as risky as using a secure website).