Bad, Bad, very bad customer care from British Airways

My wife and I bought tickets on BA to fly to Zurich via Heathrow and fly back to SA at the end of our trip from Heathrow We've app**** at the British Embassy for visas. We gave them everything, were and when we will be physically in London and when are we going to land on Heathrow. They issued our visas with different dates. We asked somebody at the Embassy who said it's ok because it is valid for the time that we will be in London. The day we we've tried to check in, the guy at BA counter said my wife can't fly. She needs a transit visa to on Heathrow. We tried to explain that we won't go out of the airport or try to book new luggage in. Long story short, we had to cancel her flight - and not just the one way via London - the whole flight. We had to book new tickets that cost us more than R30 000. Since our return, I'm trying to get a refund from BA - because I'm 100 convinced that it is their fault for the following reasons. (i) Their website said you only need a transit visa if you will go out of the airport. (ii) You only need a transit visa if you want to book in luggage. Ours should have been book in from OR Tambo to Zurich. (iii) The British Embassy didn't think we need a transit visa. We've app**** for visas - not specifying any dates. If the person at the embassy thought it is necessary to have a transit visa - he/she could have made my wife’s normal visa to be on the day before we land on Heathrow. (iv) I went through Heathrow without getting close to Customs. In fact, I had to run to get to my transit flight. I gave BA all the reasons - showing them that it is their fault. For nearly 4 months they rep**** email after email - we are not going to do a refund - without giving any reasons. I've asked them over and over for reasons. Many of their responses took 3-4 weeks. Almost every email started with: I do apologise for the delayed response. After nearly 4 months, they said, we are not going to refund you, because your wife didn't have a transit visa. Perhaps they think they are so big that they can bully individuals like us. It is a shame that a company with a turnover of billions don't want to refund loyal customers who were treated wrongly.