Standard practice

You really needed to phone BA, tell them to offload you. Then ring the TA to get them to rebook you. Done this loads of time. Silly of the TA not to tell you this.

Did BA rebook you directly? Normally, they can only offload you if you did not book with them in the first place.

Not sure what the question is.

PS Ive sent message to the moderators to correct the title of the thread. I thought you had to change your own overhead light on the plane.