Do I need a UK visa to transit through the UK although I won’t leave the airport?

I bought a British Airways flight ticket from Nigeria to Belgium to transit in Heathrow for 5+ hours with no intention of coming out on the 28th February 2020. But to my surprise I was denied boarding the aircraft: the British Airways staff insisted I must have a UK visa to transit in UK even though am not going to come out.

I know definitely there is no way they will allow me out of Heathrow airport without UK visa so he advice to buy another air ticket from other air lines because of that I slept in the airport for three days so that I will be able to buy another country ticket and a cheaper one because at that time I was advised to buy another ticket all the tickets were expensive.

When I asked what will happen to the one I bought if I can get refund he said no, which I disagreed with. He also gave me option of changing the ticket to a certain date because in my passport I have a UK visa which has not started counting so he told me to change it to that date. I told him I have important meeting in Belgium. Even to change it to that date is more expensive to buying a new one.

So now I am in Belgium I got another ticket very expensive to Belgium, this was happening 4 day ago. Please how do I go about this can someone tell me what to do and get my money back because I need my money back.