LInda, a couple of things you could try -
First, grow in large plastic pots instead of in the garden. That way you can move the pots around (or get someone else to). You could even put the pots permanently in a wheelbarrow, for the purpose.
Second, you could install mirrors to reflect light back into your garden.
Third, you can use the front yard where privacy fences tend to not be so high.
Often some plants do not need as much light as others. My vegetable bed is in the worst possible place for light - it's about a metre away from te shady side of the house, with a 2 metre high paling fence next to it. A shed hides it form the western sun and the house hides it from the east. It only gets a few hours at most (in summer) of full sun. I've been thinking of putting mirrors in, although husband said the shed is going soon. But even then - there is a very large, bushy bay tree shading it beyond the shed.
I am growing beans, bok choi, cauliflower (although they take twice as long to reach maturity), silver beet and snow peas. I have grown lettuce there, too. But my most success with lettuce has been underneath easy child 2/difficult child 2's potted roses.
If the screens are as high as that, you should have been able to object on the grounds of loss of sunlight.
I plant up a large plastic pot that's about half a metre on a side (or diameter) with a mix of herbs and salad vegetables. Red mignonette alternating with green mignonette makes a pretty border for marigolds, for example. I've planted lemon basil with a chili bush, so I've got colouful chilis changing colour from black, through to yellow and finally to red, with pale lime-green (and tasty) foliage underneath. That's only for summer, though - basil has all died back in my garden for winter.
You can also plant lettuce with pansies, so you are mixing colour with salad. And unless you point it out to people, they will never notice!
Window boxes can be good, too because they are a bit higher up and also get the warmth from the building, with reflections from the window.
Again, large pots where you can - they hold more water so the plants won't dry out.
It's not easy under difficult circumstances.
One thing about those privacy screens - it would make your visiting birds feel much safer!
Marg