@glasshalf
I am sorry your sun is being blocked out, but as has been said, the tree was there when you bought the house. Buying the house on the assumption that they would chop it to your satisfaction, was not the best idea really....
My cousin bought a house with a conservatory on it 5 or 6 years ago, and as soon as they moved in, the woman came from next door, and told her she had to take the conservatory down because it blocked her light. She said that it's a nuisance blocking her light, and she is enlisting her solicitor.
Long story short, the neighbour had no case, as the conservatory had already been up 3 years, and the neighbour had never said a damn word! When the old owner told the neighbour they were building it, the woman said it was OK, and she NEVER complained. So my cousin told her to do one.
They never spoke for a year after that, then the woman moved.
And it didn't even block the sunlight anyway! Well, only til about 9am in the summer, and 11.30am in the winter. Something like that!
So I am sorry glasshalf but I don't think you have a case. I could be wrong and maybe you can ask the council. Be prepared for your neighbour to fall out with you though.