Hi twokidtwocat
You should close your accounts when you see unauthorized debits taking place in your account. But presently, you don't need to close your accounts for this purpose. Instead, you can inform your bank to stop all the withdrawals without your permission.
Sending a letter to all the companies about removing your information from their file will be helpful. Get a written copy from them stating that the information has been successfully removed. You will have evidence about your move for later use.
Regards
Roxette