Cutting the card up does not close the account. If the wayward family member still has a record of the credit card details he could easily rack up a huge debt online.
Not only that, it affects the credit rating if the OP needs a loan or mortgage.
Write a letter to the Head Officer by registered or recorded post and keep a copy. Attach proof of delivery to the copy.
Dear Sir,
Re: Account Number --------------------
I have made several attempts to close this account and am concerned that there is still available credit of £10,000.
Please close the account forthwith. If you fail to do so and the account is used I will be in no way liable for any monies owing to your company.
I have destroyed the credit card and will not be using the account.
Please acknowledge receipt of this letter and confirm the account is closed.
Yours faithfully,
Cazdee