You have grounds for an unfair dismissal claim if your employer has dismissed you without a 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 employment to an end.
It’s for the employer to prove that the reason for the dismissal was one of the potentially fair reasons that the law allows. If an employer can’t show that it had a fair reason for dismissal, then they will act unfairly and the dismissal will be unfair.
The primary fair reasons are that the employee:
is guilty of misconduct;
isn’t capable of doing the job they were employed to do;
lacks a qualification necessary to do the job;
Dismissal may also be fair if:
the employee’s continued employment in the job would break the law;
there is some other substantial reason for ending employment which is of a kind justifying dismissal
Some other substantial reason such as a clash of personalities or failure to adapt to new working processes.
Dismissal must also be a reasonable response. Even with a fair reason for dismissal, the employer must still have reasonable grounds for believing that it was entitled to dismiss the employee for that reason.