English term (edited): shed off it

The fact it says 'off it' very strongly suggests it is literally adjoining (cf. Dominique's idea of 'appentis') — especially since the bike shed if 'off' this as well, suggesting the sort of string of often ramshackle constructions typical in a certain setting.

As this isn't probably any kind of 'hut', but a 'shed' (presumably in the UK meaning of the word?), I think 'remise' is a more appropriate term to use; mùaybe 'débarras' for something a little more informal... and emphasizing its role as some kind of 'glory hole' ;-)

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Note added at 53 mins (2013-08-06 18:54:15 GMT)
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Apologies for the wrong agreement: it should of course be 'remise attenantE'!


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Note added at 2 hrs (2013-08-06 20:03:59 GMT)
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I think 'remise' probably more safely suggests the function, rather than describing the form — and risking being wrong.

Although one often thinks of (say) a garden shed as being some kind of wooden 'hut', in the UK at least there are lots of houses with brick-built adjoining 'sheds', which as a kind of outside storage area were a common part of typical post-War council houses from the '40s to the '60s, for example.