Capetonian
You have hit the nail on the head...public perception is not good.
Take your point about company press releases in general however it is based on the CAA stats which don't lie BE have beaten BA punctuality wise (specific to LGW-JER) since 2011 I personally think that is a pretty impressive record. Obviously bad experiences stick in people's mind. BE need to look at how they deal with disruption as BE and BA stats are the opposite of what people would expect.
The problem seems to in the main be public perception. Which has to be addressed.