Listed as a no-show when I cancelled in advance of my flights resulting in issues with my refund

On October 14th, I called BA to cancel my flights for Nov 4th to 18th because I was unaware that I needed to have a transit visa just to be in the Heathrow airport between my flights with BA. I was in a panic and the agent reassured me that everything would be fine and that I would just need to contact Vitality Travel to assist with cancelling my flight. It was a premium economy seat so it was not cheap. Anyway, after waiting the 6-8 weeks that Vitality states that they take to do refunds, I called Vitality (AGAIN) and escalated the query to find out that BA had listed me as a no show even though there is proof that the flight was cancelled a couple of weeks in advance of the flight. They incorrectly listed me as a no-show and that has resulted in them not refunding Vitality and thus Vitality not refunding me. It is taking a lot of time to sort out my refund - when it should have never been an issue in the first place. I am really frustrated with the constant calls and following up I’m having to do. It’s really not fair and it’s not right to be punished for the mistake of someone at their airline. It has put a really bad taste in my mouth and I personally now feel that BA is not a reliable airline or an airline that cares about their customers or customer service.