I did write only one old fashioned letter to request a status match from CX Diamond to BA Silver or Gold some three years ago and I did get a (negative) response back in a few days.

When filling in online forms I also get replies after a few days. Recently wrote to BA Holidays and they replied as well so my experience is pretty positive with their responsivness, less so with how they respond but that's another matter.

Twitter team is annoyingly useless. A part from keeping apologising thay can't actually solve anything (e.g. failed checkins, booking enquires, etc.).