I also live in Central London, Aldgate East here. We've got Community Fibre and many areas here have Hyperoptic as well. Hyperoptic show interest to install on the website.
We're rolling out in your area
We're bringing our full fibre network to your area!
Before we can connect you, we'll need permission from the Freeholder or Property Manager - so be sure to let them know you're interested.
Check to see if you have something like this show up for you? Obviously, in my case my management team will not grant wayleave for Hyperoptic but did so for Community Fibre.
Openreach showed interest for FTTP in 2018 but my management team refused to grant wayleave.
My suggestion is to look through all the Altnets like Hyperoptic, Community Fibre, G.Network, The 4th Utility, etc and see if there are plans for your area and contact them via email. If they show interest then the next thing is to contact your local housing association management team to get them to sign a wayleave.
At the end of the day No wayleave=No fibre. Even if these companies are interested to build. You should also involve residents of your building to register their interest and apply pressure to your management.
Many places here have overbuilds with Community Fibre and Hyperoptic and some I've seen in Hackney have triple overbuilds Community Fibre, Hyperoptic and G.Network!
Contacting BT Openreach will make little different if your management doesn't grant wayleave and this will apply for all of the Altnet providers. Chances are, if there hasn't been a wayleave agreement for any of the Altnets, Openreach FTTP is an even lower probability.