This is 18 years ago so it probably isn't too relevant but I was given about 6 hours notice that my father was not going to make it through the night. I was the only one in my family not living in the U.K. so I was in an awkward situation to get back. I phoned BA explained the situation and asked the agent for a bereavement fare. It was incredible the agent said not to worry, said there were seats available on the next flight in 3 hours from YYZ-LHR asked me for my dates and gave me probably the cheapest discounted WT fare I'd ever heard of. I asked what paperwork they required and she said none would be required. I couldn't believe that an airline could be so compassionate when I could have just been some con artist trying to take advantage. I'll never forget that BA looked after me that way. It was too late when I arrived in England anyway but I kind of knew that on the flight over.
My sympathies to the OP. It's not an enviable situation to be in.