It sounds like you are getting the wrong end of the stick. Faxing the wrong paperwork is not a dismiss for cause type of offence. Unless you have a file of previous warnings and problems, long term employees are entitled to make mistakes and to have rehabilitation.
There are two types of laws at work here. Statute and Common Law.
Under statute, you are entitled to your overtime. Keep track of it. Most employers do not keep track of overtime they do not intend to pay anyway. So, your records will have weight.
Here is a link to the government body who will collect for you......
Alas, while you cannot be fired for making a complaint, often employers do retaliate so employees with a job have to consider their options.
If you are dismissed, you would be wrongfully dismissed under the Common Law. Common Law is judge made law based upon precedents. Depending on the facts, you could be owed one month of pay (plus averaged overtime) for each year of service. This involves a law suit of course but if they consult a lawyer, they may at least make an offer.
If you have an HR department, likely the business is large enough that they should know the law. They probably hope employees do not.
FYI, here is a link to the entire Statute.
The Common Law is a bit more complex as it takes reading other cases with similar facts. But, in general, my opinion is that what you have described is a mistake that is likely not to repeat as opposed to an employment offence (insubordination, theft, etc) which attracts immediate dismissal.
Here is a link to the Lawyer Referral Service. If you call and ask for employment lawyers who act for employees, they will give you names of lawyers who have agreed to consult initially at no cost. This is where facts can be discussed in detail.
For now, all you can do is wait and see what happens. At least you have some tools to keep your options open.
If you need more information, please ask. Otherwise, please rate my answer well for considering the problem.