Oh dear, that looks horrible @jamesharcourt. Possibly the foundations for the shed may also be contributing to the problem as it would displace the water formerly draining to that point? I think I would be more concerned about the bottom of the shed rotting than the tree. In time the tree roots will help to absorb more of the rainwater but I agree that guttering and a large (200 litre if you could fit it in) would help. You can't do anything at the moment though until the water's soaked away, so try not to worry too much, it'll be fine in the long term.
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Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.