Depends what you mean by double.

A quick count shows that there are 12 fare classes just for economy seats. Some are flexible, some are not. Many require advance purchase of 2 weeks or more (60 days or 90 days or more). Other like full flexible means that you can even claim a refund even if you cancel at the very last moment where BA is unlikely to fill the seat.

Once you get to two weeks before departure, only the flexbile fares are left which do not required advance purchase. Normally business travellers requiring urgent travel buy these tickets. Most leisure travellers do plan their travel plans in advance.

While BA may loose your money, you will find other airlines run the same systems. Even low cost carriers like Easyjet or Ryanair increase their prices as more seats are sold on each flight becoming more expensive as departure date draws near.