Thanks for the replies everyone.
Now I'm sitting on my Zurich flight (which is now delayed) I have some time to reply.
First of all, my return flight later this week was cancelled the other day. Fine, I rebooked onto an earlier flight. No issues for me personally.
This morning I was waiting for my car when I thought, hey I'll look at the app to make sure it was T5. That was my first and only notification that the flight has been cancelled. No email. No text.
I had a quick look to see if I could rebook and the only option available was to cancel the entire trip. So I thought I'd head to T5 anyway, in the hope that someone would be able to help. Maybe I could be rerouted, put on standby, whatever.
But at departures they now have a "customer response team" who appear all to be new to BA and all they could do was tell me to keep trying on the phone. I tried about 15-20 times before giving up.
People at the check in desks couldn't help either. Apparently not something that is possible.
I tried the check in machines and they offered me the option of tomorrow evening or to cancel.
Interestingly, a colleague was on the same flight and he got an email overnight saying he'd been rerouted via Madrid. I'll ask him later (assuming we get there) if he has higher status with BA.
But in summary, BA cancelled my flight, didn't tell me, offered no rebooking option today despite options being available, and refused to answer the phone.
What kind of business is this? We're a long way from the world's favourite airline aren't we?