If the float valve truly is 100% OK, it could be a tiny corrosion hole in the heating coil (calorifier) within your hot water cylinder. This would let secondary (fresh) water pass from the cylinder into the F&E tank, assuming the F&E tank water level is lower than the main cold water cistern level (which it often is).
If this is indeed the case, the only cure is to replace the HWC unfortunately. However I would check the float valve carefully, and also remove some water from the F&E tank to see if it gradually fills again.