Hello my name is ***** ***** I am happy to help you today. No an employee would not have any rights to claim unfair dismissal in these circumstances. This is because an employee must have been employed for 2 years before the Tribunal has jurisdiction to hear a claim for unfair dismissal.
If the employee could argue that the decision to terminate amounts to discrimination on the grounds of race, age, religion, disability, sex, , pregnancy or for raising a health and safety complain then they may be able to raise a claim under the Equality Act 2010 or possibly the Whilstleblowing legislation.
I do not think that this applies in your situation but do let me know if you need any further information.
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