Certain factions might have the clout to sort of 'own' land too - greens, gardens, stables & space for security might exist for the very powerful. The balancing factors would be of course that most often no one but the city rulership had real control of the land and every cottage or family probably paid taxes.
If you were a knight with a manor in the city you might have grazing rights or clout enough to stop hangers on from building off your home. Your use of the land might deter builders.
If you had no prestige its unlikely you'd get much support because the new building probably meant more taxes in one manner or other. Green space would be at the whims of the city and likely trampled and plundered unless you had a wall around it or something.
I like your hand drawn look. How hand drawn is it?