remember they are connected by a small pipe, you still have to fill both tanks otherwise you will get one tank full and the other will be well less than half full until the liquid levels have enough time to equalize

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1970 Mk2 Cooper S under restoration

Just had the same issue as GuamMini - ran out of fuel, with LH tank empty and RH tank half-full but not flowing to LH side to equalize level.

Turned out to be a blocked breather hole on the top of LH tank. Fuel cap was non-vented so enough pressure built up inside the LH tank to stop fuel moving under gravity, from RH tank.
Timmy201 had already suggested this as a possibility but I thought was very unlikely, given the diameter of the breather tube.... apologies Tim, you were right.