orbitmic

Exactly. And I can only reiterate my earlier advice - providing a testimony to the police is far, far more important than providing a testimony to BA. Something the OP sends to BA will be worthless in court (unless the OP was planning to fly back on his own expense to attend court if the matter goes to trial at all?) whilst a proper testimony to the police is the only way to increase the chances that the culprit be prosecuted (which, from the op's words would be right) and that his testimony can then be given weight when that is the case even if he cannot attend court in person.

By contrast, BA do not actually need a separate report to ban the person from flying. If that passenger is condemned by a court for assaulting a BA member of staff, this will be more than enough for BA's purposes.

I mean sure, feel free to "also" write to BA if you have time on your hands though it won't make a difference that you do, but focusing on that is just the wrong priority and if it comes at the expense of a proper visit to the police, this explicitly does a disservice to the victim who is less likely to see justice served as a result.

Effectiveness is key here, and this is too important not to get your priorities right, and BA is just not it.