OP, you have my sympathy. Not everyone is a frequent traveller and knows the ins-and-outs of airports & flying, and I think what you did was an easy and logical (but ultimately costly) mistake to make. The flight was going to be late, that was communicated to you, and the logical conclusion was that you shouldn't waste hours sitting about an airport, and just leave for the airport a little later.
As fliers we have a wealth of data and information available to us at our fingertips through BA's website, app and 3rd party tools like FlightRadar and so on. In days gone by, most people wouldn't have had any clue about a delay until showing up at an airport check-in desk to collect a boarding card. They'd have gone by the scheduled departure time and simply have had to simply 'suffer' the delay and go to a lounge or find somewhere to sit and have a coffee.
Today, not only are there numerous sources of information on both the nature and length of delay, but you can even find out the specific registration of the aircraft due to operate your flight and see exactly where in the world it is. A little bit of knowledge can be a dangerous thing. Sometimes we have too much information available to us, and lead to wrong conclusions as a result. The lesson here being: unless it's explicitly communicated otherwise, always show up for the originally scheduled flight time.
To give a recent example, during the "Snowmageddon" for a few months ago, at OLCI, my IAD-LHR flight was showing an 8 hour delay (originally scheduled to depart 22:00, now departing 06:00). The prospect of 8+ hours sitting in Dulles with nothing open didn't thrill me, and I nearly panic-bought a non-refundable hotel room at the airport to wait it out. But I stopped short of pulling the trigger, and lo-and-behold, at around 10 hours prior to departure, they had changed the aircraft operating the outbound from London and we ended up departing as originally planned. So all of this data that is now available to us should be read as "for information only" and taken with a healthy dose of salt, since things are often very fluid in the hours leading up to departure.