Hi.PJ67.
I'm only an ex-ppl, but I would suggest that your 'awful landing' at Heathrow was simply the result of a nasty crosswind. If this is the case, it is very common practice [even in a 747] to land with the aircraft well banked into the wind, therefore resulting in your view of the grass etc.,
This prevents the aircraft drifting off the centreline, and is absolutely no cause for alarm, and is perfectly normal given the prevailing conditions. I
I can, of course, understand your concern, which, without meaning to be patronising, is simply due to your inexperience.
I have travelled frequently with nearly all trans-atlantic carriers, and always go BA if possible. Happy future landings.