Carb icing has been around from the beginning based on the service bulletin below (From The Series One Club Newsletter, 9/95). The bulletin indicates crankcase ventilation can contribute to icing, which suggests that a malfunctioning PCV system may be a culprit.

Combustion produces lots of H2O, and any blowby will add water vapor to the crankcase. The flow with PCV is supposed to be from the oil filler tube thru the PCV valve into the intake manifold (not thru carb), and from the air inlet to the rocker arm cover. If the PCV valve is blocked or removed (which can increase blowby), but the hose from the rocker arm cover to air intake is functioning, then the flow will reverse and the crankcase will vent thru the rocker arm cover and then thru carb. The humid vapors going through the car could contribute to icing. Per Trevors suggestion a switch from the oil-bath air cleaner to a pancake filter would eliminate this if the hose from the rocker arm cover to the air inlet was removed at the same time.

The above is theoretical since I dont have any personal experience, but checking the PCV system may be worthwhile. If your PCV valve, etc is removed or blocked, then you have a crankcase vent system similar to that described in the bulletin. Either get the PCV valve functioning (preferable), or vent the crankcase directly to atmosphere using the vented filler cap and rocker arm cap. A short-term fix is per the bulletin.

Caveat: An accompanying note with the bulletin mentions that Rover switched to a free breathing system in mid-51 which eliminated the hoses. Rover made a heated carb. optional on early SIIs before PCV, so the switch must not have been the sole solution.

 
Internal Service Bulletin (Defect) No. 50021
January 1st, 1951
 
Models. 1948-51 LAND-ROVER
 
Complaint. Loss of engine powe, with black smoke issuing from the exhaust
pipe; sometimes the engine stops completely. The engine can be restarted if
it left stationery for five minutes.
 
Cause. Ice formation in the carburetter choke.
 
Remedy. (a) Raise the under bonnet temperature by blanking-off part of the
radiator grill panel, especially below the R.H. headlamp. By experimenting
with baffles of varying size a cure can usually be effected. If trouble is
still experienced:
(b) Disconnect the top rocker cover and crankcase breather pipes at the
carburreter intake elbow and allow them to breather to atmosphere: blank off
the two holes in the elbow by means of short lengths of rubber tuing plank at
one end with suitable plugs (i.e. bolts) and secured to the elbow with hose
clips.
 
Note 1. It is most important that the breather pipes are reconnected to the
carburretter elbow when warmer conditions return.
 
Note 2. Remedy (b) must not be used where a vehicle is operated under dusty
conditions: acure must be effected by blanking off the radiator