A causal reading of this thread might leave someone with the impression that it's a minor miracle when the BA207 operates, but reality is more mundane. Here's the most recent Reliability Data from Expert Flyer:


Over the last two months, it's been scheduled to operate 61 times and cancelled 4 of those, about 1 in every 15. Are those good figures? Absolutely not, they are below what either airline or passenger would want or expect, but the simple fact is that for a passenger on the BA207, the most likely outcome by far is that the aircraft operates as expected, and arrives within about an hour of scheduled time.

However, cancellations clearly happen, and this route is more frequently impacted than others - as I believe has been noted upthread, one obvious reason for that is that there is an abundance of alternative options which BA can book you on, albeit many will have an additional stop e.g. at JFK or PHL. They will generally prefer to book on oneworld (so American Airlines for the USA leg) but are obliged to book on non-oneworld carriers if necessary. Unless your dates coincide with some major event, it should not be difficult to find something that gets you there on time.

It's been a while since I've been in the lounge at Galleries South, but I assume they still have the Customer Service desk just to the left of the entrance, in the event of a cancellation, they would be my first point of contact. I believe that (unfortunately) a lot of ticketing functions have been moved from the agents at Heathrow and it's mostly (all?) done by the call centers now, so I'd also get on the phone at the same time if the app isn't already showing a suitable alternative rebooking. I would also reach out to the community here, with specific details, and I've no doubt you'll find lots of people who can suggest alternatives that will work for you.

Enjoy your cruise!