My first reaction was "what's the problem" - it's so much more open than my shaded garden. But you mean large trees?
Looking at the google map, they're to the NE and N, so will be casting shade like that in the morning. As the sun moves round towards the south, the shadows will be getting shorter and being cast more on the neighbour at the bottom of the garden.
What will cast shade for most of the day will be the house.
However, looking at the photos, the shadows of the fence are quite short, so the sun is quite high in the sky, and therefore to the SE rather than the E, so it doesn't really tie up. I'm quite puzzled.
I note that you're in Kent. I'm in the frozen north, and I can remember in our last summer, which I think was 2006, where we got to about 30deg, I was so glad of my cool shady garden.