Jayy:

Before you fight this you need to review the circumstances of the payment not the various things you have been informed by different Halifax staffers.

You think you made the payment "1 day too early", the Halifax computers (note not people) think you were late.

So what was your payment due date, what date can you prove the payment left your payment account, how many days does the CC statement say you have to allow for the payment to reach your CC account and what date does your CC statement show the payment was actually credited to your account?

Once you have analysed that you can identify where the problem lies.

If you can prove Halifax have blundered what you have been told about the marker being wrong is not true and can be dealt with through the complaints process.

If however you made a payment which was credited before the next statement date (is that what you mean by "1 day too early"?) then Halifax are right. In that case too late for you on this occasion but this is best avoided in future by making the minimum payment by direct debit.