Employees have the basic right to not be dismissed unfairly by their employers. However, this does not prevent employers from dismissing employees, and claiming that the reason for dismissal was a fair one, when the reality is much less straightforward.
There are very strict timescales for making a claim. Your case must be registered with ACAS, for Early Conciliation, within three months (less one day) of the date that your employment ended. If this deadline is not met, then your claim will likely be time-barred.
It is, therefore, vital that you instruct a solicitor as soon as possible so that they can advise you on whether or not you have a claim and, if so, how best to pursue it.