BA refuses to return money they took through their systems error.

I recently used the BA online manage my booking service to try to change a flight time. After following the usual pathways through the system I was shocked when my confirmation came through with my previous flight times. Worse BA had charged me over £200 to change my flight to exactly the same flight! I assumed it was a glitch and called the refund department. They refused to refund me saying I had bought the same flights but at at present day price . I then used the customer relations form who told me to go to refund, who told me to go to customer relations! The worst part is they have no customer service as such in this country. They rely entirely on AI and people in India using AI. This means tgat when the system makes an error that the AI complaint system doesn’t understand nothing can be done and nobody can be spoken to! It’s crazy!! I can’t believe I am paying over £200 to sit on the same fight as I was before. Even the staff at Heathrow were totally bewildered but said there is a total break down in any customer service.