They are not held on your MyBT account but BT will be aware that they sent either a letter or email to you and when it was sent.
You have 30 days from receipt of the email/letter to inform BT of your intention to leave because of the price rise.
This does not mean you have to leave within that 30 day period. You do not and should not tell BT when/date you are moving.
Once you have notified BT of your intention to leave you would then need to take out a contract with another ISP inform that ISP of when you want your "new" connection to start. The new ISP will notify BT of the date and take care of the move.