If you have a thin 32 mm spanner, you give the spanner a belt with LR tool no 1 in the direction of rotation and the nut will come loose (or should come loose). Then you just spin the fan off. I once had to hold the belt with a pair of mole grips but this is very unusual. The LR manual does show another tool to hold the pulley by the 4 x 10mm bolt heads, but I haven't needed to make one of those yet. If the belt is broken and gone one might need the tool, although we have old belts lying around that can be used.
ps the reason I used an old leaf spring is that it is very strong and does not open out easily.