There are two ways around this.
Whichever way you go, You must run the speed tests regularly, and keep a record of the results. (speedtester bt.com)
1. Formal written letter (not e-mail) to CEO, copied to the Chair of the Remuneration cttee. and the Chair of the Audit cttee. All names available on their website under Corporate Governance.. That - hopefully - gets the issue referred to the good guys in the bosses problem solving part of BT. They assign a case manager who stays with the problem all the way thru to resolution.
2. Find a friend of yours who works for BT. BT employees can refer cases to a special unit. Again, they assign a case handler.
If BT cannot improve your speed you'll find out via one of those routes.
NB. Whilst BT maintain that they cannot increase speed in many cases, their Chairman lived in an out of the way (but smart) village miles from the Exchange. Once he complained, surprise, surprise, his little village had a miraculous speed increase.