I'm in Worcestershire but the exchange is part of the Birmingham director area, which goes somewhat over the border into Worcestershire.
We were an early area for FTTC, when most of outer Birmingham was done, before several areas that are now FTTH or planned to be.
On the BT checker map we are lumped with a couple of parts of south Birmingham plus parts of Warwickshire and Worcestershire (which are not part of Birmingham area), as an island of no Full Fibre, whilst other areas less populated around us are on the list.
BTW, I had another EE flyer again telling me I can have full fibre now.☹️