I suggest you write a letter in her name (MIL must sign it) with the care home as the current address.
Dear Talk Talk
As I have moved in to a care home I wish to cancel my account for 10, Downing Street, London with immediate effect.
The phone number was 000 0000 0000
The last 4 digits of the bank account used to pay the direct debit is 1111
Please send the closing bill to my current address,
Yours Faithfully
(Full name).
Send it to:
TalkTalk Correspondence Dept.
P.O. Box 346
Southampton
SO30 2PW
I would send it be recorded or registered post so you know they have received it.