if the minutes of the GM are issued and it states the percentage of the vote, say 60%, and that the resolution is not passed to appoint as director, and the director is therefore removed at Companies House, could this be challenged?
It is not quite clear what you are saying now.
At first you were talking about a breach of the shareholders' agreement. You have moved to a breach of the Articles.
The articles say how a director is appointed. If the appointment is valid under the articles, then it is a valid appointment in company law. That it may be in breach of the shareholders' agreement is of no consequence.
In any event, I doubt that Companies House would be interested. A director's appointment is registered by a form completed and submitted by the company secretary and signed by the appointee.
Companies House will rely on the certificate that he has been validly appointed. Someone aggrieved by the appointment would have first to challenge it at a meeting of the company, and then at court.