BA have had a couple of terrible maintenance oversights (757 wing panels, 777 fuel leak to name the worst) but have a reputation for quality maintenance rather than a reputation based on a couple of mistakes.
I think is false to suggest that BA is known primarily for bad maintenance within the industry as this is clearly not the case.
Going back on topic , our QA's are a mix of Licenced and non Licenced staff. As Genghis says, there is no licence as such for a QE - just helps if they've done that role to appreciate the different aspects of the trade.
I've no experience in the design/production side of things but i'm lead to believe there is no licence QE qualification in that field either.