I think the credit card charge back may now be the way to go.
This morning I had an email from UK trade support, copying me in on what the TA claims to have sent to them, but it doesn't mention how it is progressing.
I called the number on the email and they denied that Gotogate are on their books and gave me a number for BA CR. It was a staff only line and they gave me another number. I have been on hold for 10 minutes.
Generally BA's advice is go back to agent, but I get nowhere!