The clause about the precedence of the SHA must be read with severe caution.
The Articles govern the relationship of the company with the outside world. The outside world is entitled - entirely - to assume they will be applied. In oarticular an outsider must be able to identify directors from Companies House, and to be able to act upon that information. This is a fundamental of company law.
The clause within the SHA can _only_ apply to regulate the actions of shareholders when voting. If it purported to impose such a restriction so as to attempt to invalidate the actions of the company, I would need convincing that it was effective.