Yes, the ground plane is of substantial influence.
If I understood correctly, the length of a quarter-wave mono-pole is based on having a proper groundplane because the ground plane in fact serves as the counterpoise of a half wave di-pole.
From this perspective, when having a proper ground plane the length of the mono-pole should be exactly one quarter-wave length (velocity factor not taken into account).
Here in the Antenna length for 868 and 433 MHz topic a general rule of thumb is mentioned to use 5% for the velocity factor.
86.3mm x 0.95 = 81,99mm which exactly matches your 82mm.