Any airline wants to get maximum revenue from a flight. They will sell ALL the seats, even the ones in the first class cabin. So who gets the first class seats? That's going to depend; if the flight has at least 14 seats still available on departure it is very unlikely anyone will get an upgrade. Beyond that it depends very much on how the load is balanced. They will start by moving people from World Traveller to World Traveller Plus and that will push people into Club and that will push people into first class seats with club service. Then again if there are seats available in World Traveller but Plus is oversold then the some Plus passengers will be moved to Club etc. etc. As others have said the first choice for upgrades are "premium" Exec Club members but that's not the only criteria. My "best" upgrade on BA was when I was coming home from Denver before Plus appeared; I had THE cheapest economy ticket, no status and I wasn't the best dressed yet there I was in Club. I can only guess they only needed one upgrade. I've had upgrades from Plus to Club when I've paid Plus out and Club back, still no status. I have wondered if some of those have been an attempt to tempt me to buy Club round trip (it's worked, very occasionally I've done that).
I think the most obvious example of selling ALL the seats was in the short period when BA were operating Manchester/Los Angeles. Until about 2 days before departure the flight was full. Then 2 seats appeared available for sale in about 3 or 4 selling classes. I did a little experiment. It didn't matter which class I booked the number of seats went down in all of those classes being shown as available for sale. In other words BA reckoned the could accommodate 2 people and just wanted to fill those - they'd work out who to seat where on the day.