Your local council should be able to tell you either by phone or on their website

i seem to remember that we have 'no right to light'. But I may be wrong.

if you find you cant do anything then welcome to the world of shade plants. I was dismayed when i realised how shady my garden was but the plants i am able to grow far exceeded my expectations.

I don't think there is any restriction on what a person plants in their garden. If you say anything, however polite and tactfully put, some neighbours will take umbrage and become 'difficult' to deal with. Why a Walnut tree? Slow growing....so she will have to wait to lose the hated sight of your house....very strange. Another question......is early morning sun very important? The sun moves through a quarter circle over the year so shadow situation changes. What the roots might do is more of an issue.

Take some consolation in the fact they haven not planted the dreaded Laylandii!

As long as it is a walnut and not a black walnut. If it is the latter you may have problems in years to come with the toxins affecting quite a few plants. the toxin called juglans.

I was going to say that some forms of Walnut produce juglone which is toxic to other plants.
From Wikipedia
However, different walnut species vary in the amount of juglone they release from the roots and fallen leaves - J. nigra, in particular, is known for its toxicity, both to plants and horses.[17] Juglone is toxic to plants such as tomato, apple, and birch, and may cause stunting and death of nearby vegetation. Juglone appears to be one of the walnut's primary defence mechanisms against potential competitors for resources (water, nutrients and sunlight), and its effects are felt most strongly inside the tree's "drip line" (the circle around the tree marked by the horizontal distance of its outermost branches). However, even plants at a seemingly great distance outside the drip line can be affected, and juglone can linger in the soil for several years even after a walnut is removed as its roots slowly decompose and release juglone into the soil.