The Forest Hill exchange on Stanstead Road does have fibre enabled, but you need to live somewhere where the cable has been laid.
With BT, in some bits of SE23, we have access to a pilot with fibre running all the way to the house, while in others the more standard "fibre-to-the-cabinet" is available.
I'd definitely say it's worth calling BT to check.
In response to the other poster, Virgin Media fibre is available in "some areas" of SE23, but coverage is far from comprehensive.
Here's a handy link which shows with minimal jargon what the coverage/options are: http://www.samknows.com/broadband/exchange/LSFOR