Most likely either one shoe has seized in position, a spring is broken, or there is a lot of foreign material (most likely oil from a leaking seal) in the brake that happens to affect one shoe and not the other (or some combination of these). Note that small amounts of oil will cause the shoe to grab rather than slip.
I would be inclined to remove the drum and see what is going on. On most Landrovers this can be done without removing the prop shaft, and I think this is the case for the D1.
John
John
JDNSW
1986 110 County 3.9 diesel
1970 2a 109 2.25 petrol
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