Hang on - I had assumed it was the mower cable you cut through - are you saying it's the cable supplying the shed?
In your pic the fusebox looks fed via a plugtop in a single socket, if it is did you check that fuse in the plug.
Hope its not a live supply out of the board with a LIVE plug on it, so be carefull.
If the plug is feeding the unit, and the fuse in it had gone, I'm assuming that nothing would work ... but the garage lights do
What is the plug for do you know, it may join to the wire going to the shed.
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