I imagine the concensus, peterjameswhitcombe, will be that it's not going to be ideal. The sun tracks from SE to SW at its most powerful so south facing is the best. If, by chance, you happen to have a smaller south/south west facing site, it would probably be the better option.
My lean-to is built against the west facing wall of my house, on a flat area carved out of the hillside. Mature trees on the rising ground, mean it is fairly well shaded in summer. and it only gets full sun when the day has progressed enough for it to clear the end of the house. It gets shaded again as the sun drops behind the trees on the hillside.
The amount of time spent in the sun obviously changes through the year, but the stone wall absorbs the heat and it can get very hot in mid summer, enough to make my fuchsias uncomfortable, so I usually shade paint the roof. I bubble wrap in winter and have a fan heater set on frost free which only comes on when necessary, so fairly cheap and gives peace of mind. It is is pleasant to be able to potter in there in relative comfort, even in winter.
I use it for overwintering tender plants, raising seedlings and growing on, and grow both ornamentals for my pleasure as well as veg plants and tomatoes.
If your NE site is all you have, then you will still get some sun early in the day, so it could still prove useful and a source of enjoyment, dependiing on where you are. My GH is fairly protected from the prevailing westerlies, and from the east too, and it is the easterlies that bring the most bitter weather here. Northerly winds are relatively uncommon, but again my GH is shielded by the hillside, while yours may be fully exposed to both cold aspects and this, rather than the light alone, may be limiting.
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Ferns would be happy there, but not much else.
Billericay - Essex
Knowledge is knowing that a tomato is a fruit.
Wisdom is not putting it in a fruit salad.