A few years ago MrD and I had the pleasure of having dinner at the Friars Club, they have a dress code for the restaurant. MrD and our host were suitably attired, the two gentlemen who weren't wearing jackets were given loaners, huge jackets that had probably been there since biblical times - they looked better without them.
BA is not a private members club, air travel should be comfortable - no dress code should be required (however nice the dress may be !