Misconduct is a valid reason for dismissal, though not typically on the first offence. It more typically follows a series of documented warnings (for misconduct), the last of which would be a Final Written warning. Failure to improve following such a warning may lead to dismissal with notice.
Gross Misconduct means a fundamental breach of the contract by the employee, ajudged so severe that the employer terminates the contract without notice.
The employers policy ought to state what the appeal process is - there is no harm in following that through.
If that still leads to conclusion that the employee believes to be unfair, the remedy is then to take the matter to an Employment Tribunal for unfair dismissal, however this is not possible unless the employee has at least 12 months continuous service.
The only other possible remedy (if the employee doesn't qualify to put the case to ET) would be a civil court action to seek to show that the gross misconduct dismissal without notice was inappropriate, and that damages should be paid based upon the notice pay denied. Frankly that doesn't sound worth the effort.