Height alone is not what counts
The CX height limit is actually on the low side Singapore airlines is arround 165 cm. But a height limit does not really tell the story.
Functional reach and leg length are what is required
The RAF currently requires the following:
Pilot:
Weight: 56.8 - 94.0 Kg (ejection seat limits)
Functional reach (shoulders to thumb-tip):
740 - 900 mm
Sitting height: 865 - 1010 mm
Buttock knee: 560 - 660 mm
Buttock - heel: 1000 - 1200mm
A combination of the minimums would be very ape like!
Note a height limit is not mentioned but a survey of RAF aircrew carried out in the past would suggest a lowest likely height of 165 cm.
You need the leg and arm reach to adequately achieve full control deflection and to reach all vital cockpit controls (the upper military limits are to avoid leaving legs and arms behind on ejection).
It should be noted that a height of less than 160cm does not preclude holding a class one medical, (but my 8 year old daughter could also qualify for one of those). However, it may well prevent someone from acheiving full rudder deflection whilst operating the throttles and maintaining the required eye position, as needed in any landing or takeoff performed near the crosswind limit. Or passing an aircraft rating on a large public transport, (which can also require considerable strength to fly under adverse conditions).
As an earlier thread stated, aircraft are designed around the 95 centile range. It is an unfortunate fact that not everyone is the right shape to control one, and there has to be a limit somewhere.
This limit is currently 160cm in CX.