No bar for UK citizens, but if you visit since around 2020/2021 it will mean you can no longer go to the US on an ESTA, you would need to get a full US visa. But even before that BA didn't go to Havana.

You could ask that of any destination tbh, why does BA not fly to X. At the end of the day BA decide where to deploy their assets based on where they think they will make the best return, and presumably they have determined that doesn't include Havana.