Is it reasonable to dismiss an employee at the behest of a third party, without considering whether the request of the Third Party is justified?

No, says the EAT in Bancroft v Interserve.

Many employers seek to rely upon third party pressure without further ado. This is a warning to employers that they must make all due and proper enquiry as to the circumstances giving rise to the third party pressure and if necessary, to consider whether there is anything that they can do to get the third party to change their minds thus allowing the employee to resume work without dismissing. If the third party will not be swayed, the employer is duty bound to seek alternative employment for the employee before moving to dismissal.

Dean Morris