Hi
Also had this problem at the beginning of the month-hard to track down because it only affected emails from some people, others got through.
As you ahve a btinternet address are youa bt customer because if you are you should complain. The problem as pointed out relates to the fact that much of the BT mail address lists are still dependent on Yahoo and the companies do not get on. BT will try and blame Yahoo who will pass the buck back.
Look up the postal address of BT HQ and send a letter , yes a real one, to Libby barr head of Custoemr Services and after a few days you will get a call back from 'executive complaints' .
They will save you the BT India experience or the untrained UK based team who have just taken this sort of thing over and while they may not get it sorted out they are as good as you are going to get in this rather sadly fading away organisation