Help locating new greenhouse

I moved into a rural location at the end of last year; most of the upheaval is over, and I'm now looking to buy a decent greenhouse (8x10 or 10x12 depending on cost), and wondering where to locate it in my garden. I've read up, general consensus seems to be an E-W orientation, but avoid locating near/under trees. That's a problem for me, as my garden is surrounded on all sides by mature trees of different varieties (including Scots pine, lime, holly, sycamore, beech, oak).
I have plenty of room to the north-east, east, south and south-west, but all these areas have trees on the boundaries; the eastern boundary seems to be mainly youngish damson trees, possibly self-seeded. In the absence of a 'best' option I suspect I'll have to choose the least-worst option, I'm hoping that someone might be able to tell me what that might be please.
Plan below shows plot and some planting that was needed for planning permission.
Liz
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I have a small greenhouse that is under a large apple tree (planted very close to the west side of a long side of the greenhouse). There are other trees to the north and a hefty wall also to the west side (more than 20 feet high). The greenhouse warms up with the morning sun, which falls on it from dawn until about midday at this time of year. This morning it was 30 °C. at 11 am, even though we had had a frost overnight, and the automatic roof vent was wide open. After that it it in the shade. But the warmth stays in the greenhouse all day. And with the shade of the tree and the wall, I don't have to paint the glass with anything. I have grown tomatoes successfully in it this summer.
If you live in Derbyshire, as I do.
Thank you for replying Pansyface.
I've certainly got room to put a greenhouse on the western side (south of the Scots Pine and Beech) but there are some tall trees on my neighbour's property (in the south-eastern chunk that's missing from my garden) which unfortunately would restrict the amount of early morning sunshine I'd get.
Scots Pines will usually cast the least shade of common trees so it might be a case of choosing the least worst option. I have always located my greenhouses N-S to get an even amount of sunlight to each side. I also planted a dwarf apple tree near the South end which means there is lots of light early on the season when it is most needed but provides some shade in Summer when it is in full leaf, negating any need for artificial shading. Works well.