https://en.wikipedia.org/wiki/Honey#Preservation in particular mentions gluconic acid and hydrogen peroxide produced by the bees' glucose oxidase, and https://en.wikipedia.org/wiki/Honey#Medical_use_and_research also mentions its content of methylglyoxal, which damages DNA and cross-links proteins somewhat like formaldehyde, thus killing microorganisms; mãnuka honey is required to contain at least 85mg/kg of methylglyoxal, according to https://en.wikipedia.org/wiki/M%C4%81nuka_honey. I suspect that there is a great deal more research on the topic.
It's disappointing to see such a low-quality article on the BBC website; I generally regard the BBC as a reliable source.