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If you are referring to appealing a decision made as a result of your employer following their disciplinary and dismissal procedure in which you were dismissed then there is no strict time limit in which you must let them know you wish to appeal other than that it must be done within a reasonable time and withot unreasonable delay.
If you are referring to bringing a claim at an employment tribunal for unfair dismisal then you must issue the claim within 3 months (less one day) of the date of your dissmal. In some circumstances this may be extended at the Tribunal's discretion.
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