I was trying the opposite (trying to do London-Paris on Sunday) and was also bemused by lack of availability, not just on BA but on every other provider from Eurostar to Easyjet. Having now made the journey (by E*) I think I understand what was going on. Engineering works at Gare Du Nord this weekend meant that the high-speed lines into it were unavailable. This means that a lot of E* trains didn't run this weekend and those that did had journey ties 90 minutes in excess of the usual. The cancelled trains alone will have taken 1000s of seats of capacity away some of which will have gone on to the airlines whereas others will have opted not to travel.

If my theory is correct, next weekend should show similar problems since I believe the same engineering works are taking place then, with the same effect on E* journey times and schedules.