If the Cable is white as you say i wouldn't have thought it will have any "Wayleave" via BT. The builder would have provided a route for BT and the engineers would have used it to run the cable never expecting you to do what your doing with your flat.
Check the route, find how the building...
Openreach will charge for a shift of equipment / cable.
A few questions...
Where is the NTE or external cable termination point ?.
Is it external duct feed or overhead ?.
Is the cable you wish to shift white or black ?.
Had the same problems and switched to a "newer" timer. Problem solved but this is the second time I've changed the timer in the last 3 years.
Simple job as said before once the power is turned off.