Green manures are plants which are grown to improve or maintain the soil and reduce weeds. If soil is left bare it loses nitrogen to the air, and rainwater leaches nutrients out of it and erodes it. Around here (Scotland)if soil is left bare it quickly gets invaded by rosebay willowherb and couch grass.
Some green manures are legumes, such as lupins, clover, vetch and trefoil. These enrich the soil with nitrogen, especially if they are cut and mulched or dug into the soil. The amount of nitrogen fixed is roughly proportional to the yield of the green manure, but at low temperatures, legumes take more of their nitrogen from the soil, and less from the air.
I feel that there is probably very little benefit to growing legume green manures over winter in cold places like Scotland, unless they grow for a few months in Spring and Autumn as well. In Aberdeen, green manure vetch and field bean, planted in autumn grew very poorly, and left a lot of bare soil. I suspect that more nitrogen leached out of the soil during the winter than could ever have been replaced by the vetch or field beans. A mixture of legumes and non-legumes will actually fix more nitrogen than a legume monoculture. Undersowing of legumes such as clover with summer crops allows them to become well established before the winter sets in.
A spring sown legume green manure will fix plenty of nitrogen, but this will take up space in a small city garden, and it may be more worthwhile collecting compostable materials from outside the garden (e.g. ask your local greengrocer for spoiled fruit and veg). On the other hand, if you are leaving the garden for a few months, years etc, legume green manures are a great idea.
Another problem with legume green manures is that when they are dug into the soil, much of the nitrogen leaches out, especially if it rains heavily been digging and sowing. Sowing too soon after digging in green manures can inhibit seed germination, but this won't matter if you are planting onion sets, seed potatoes or other tubers
I think that a better way to use legumes such as clover is to have an area of grass and clover lawn, mow it regularly and use the clippings as mulch or for compost. The 'lawn' could be the path in between raised beds, or a border around the garden, to soak up and recover nutrient run off. In many intensively managed city gardens, the problem is not a lack of nitrogen, and other nutrients, but a surplus of them, to the point where the garden becomes a pollution hazard. Many gardeners buy in vast quantities of manure and further enrich their soil with compost from bought in vegetables. If the weeds in your garden are thick, lush and green, and include lots of stinging nettles, docks, and other nutrient loving species, it could be a sign that you are feeding the weeds more than the vegetables. I would cut back all the weeds and add them to the compost heap. It is an error to see this as "disturbing a wild place": the wild place has already been disturbed by eutrophication (an over supply of nutrients). Cutting and removing the vegetation restores the balance. You may even get more interesting wildlife as a result.
Other green manures, such as mustard and ryegrass, cover and protect the soil, and take up nutrients which would otherwise be leached out of the soil. When the green manure is dug into the soil, the nutrients are released. These crops are good to grow over winter.