Thanks UKTravelBear. I had meant that the details I had passed to BA were correct rather than the ESTA itself. I'm 100% certain on the ESTA.

As it happens I was passing through LHR today so asked at the first desk if they could print me a boarding pass to save time in the morning. She had to make a call to someone who answered the call "Selectee" something or other and then was able to print the boarding card. No sign of SSSS on it though.