You would have to take legal advice before dismissing anyone.
On the face of it, it sounds reasonable, but your procedures have to be fair. You would have to have a formal meeting to discuss it and you would have to give them a chance to air their side of the story. You would probably have to give the person a written warning that this was unacceptable and if it occurs again they will be fired.
Does the person have a contract of employment? Do you have disciplinary procedures in writing?
I would guess that the Employment Appeals Tribunal would probably have sympathy with the employer but would decide that dismissing them was unwarranted.
Brendan