You are most likely to be being provisioned with FTTP rather than FTTC - at least according to an old map of York that Openreach published - back when FTTx was initially being trialled.
The "FTTC/FTTP Trialist Working Group" minutes from September 2010
, page 39 should give you a clearer picture. All the cabinets surrounding you seem to be for FTTP.
The downside is that BT are *horribly* delayed with FTTP compared to FTTC - and *that* is probably why you aren't getting any availability while the exchange itself has long been ready.
The best checker is the BT Wholesale one: here
There has been lots of talk about the York fibre ring, but it hasn't yet turned into quantifiable action for residential use.
York is combined with North Yorkshire in the BDUK bid, so you might get news on their homepage