You have grounds for an unfair dismissal claim if your employer has dismissed you without a legally fair reason.
The test isn’t unfairness in the common sense meaning of the phrase; it’s whether there was a legally fair reason to bring your employment to an end.
It’s for your employer to prove that the reason for the dismissal was one of the potentially fair reasons that the law allows. If your employer can’t show that it had a fair reason to dismiss you, then the dismissal will be unfair.
The primary fair reasons are that:
you are guilty of misconduct
your aren't capable of doing your job
you lack a qualification necessary to do the job
your role is redundant
Dismissal may also be fair if:
your continued employment in the job would break the law
there is some other substantial reason, such as a clash of personalities or failure to adapt to new working processes, serious enough to justify dismissal.
Dismissal must also be a reasonable response. Even with a fair reason for dismissal, your employer must still have reasonable grounds for believing that it was entitled to dismiss you.