After declaring an emergency, if they landed at Heathrow, that was at the pilot's discretion or due to limiting factors like runway length at Gatwick and the weight of their plane. The article is light on detail but they circled over Kent as well, so the pilots must have thought it was safe after shutting down the engine. Not sure what the "black mark" is exactly.
Gatwick and Stansted can take any plane just as easily as Heathrow, but has less on ground resources to fix the plane.
I'd guess they knew it was safe and it's easier to deal with a plane full of pax at your originating airport than diverting to STN (where there's no BA ops) or LGW (BA have ops here so could have worked).
BA did fly from STN in 2017, at the time of the incident - they served short haul tourist routes like PMI, AGP, FLR, IBZ.
That said BA earned a hell of a black mark when it chose to divert to Heathrow rather than Stansted or even Gatwick when its engine was on fire [1]. Not as much as when Air France decided to divert from Lebanon to Damascus in the middle of a civil war rather than Cyprus because it was cheaper [2]
[1] https://www.standard.co.uk/news/london/ba-flight-returns-to-... [2] https://globalvoices.org/2012/08/26/france-an-epic-flight-fr...