The black spots are called Tar Spot and are produced by the Tar Spot Fungus (Rhytisma acerinum). As the scientific name implies, they do not confine themselves to sycamore trees, but to all the Maple or 'Acer' family. A closer look shows how the spots got their name, as they really do look like splashes of tar.
Despite the nasty appearance of this fungal infection, the trees are rarely affected to any great extent and seem not bothered at all - sometimes the infected leaves will fall a little prematurely. The fungus is returned to the soil in autumn and lays in wait for spring to be taken up once more by the growing tree, ready to continue the cycle.
Trees growing in towns and cities are less likely to be infected because their leaves are more likely to be cleared away when they fall in the autumn, thus the life cycle of the fungus is interrupted.