I have recently seen news of a 4G wireless broadband operator called Relish. They opened in central London in June.
I contacted them and they do not yet provide in our area, but you can go on their site and on the page where you check coverage by postcode (https://www1.relish.net/athome#inyourarea), you can vote for SE16 7TQ. It may be worth everyone who is concerned about the broadband doing this so we may get more choice.
I contacted hyeroptic, but never heard back from them.