In your position I would search in the hiking maps for springs. They are usually located in forests and there shouldn't be contamiated with anything. The water should be safe to drink.
The stream should cross not too far away a meadow that is a bit higher located than the surrounding terrain. Like this it stays rather dry and there will develop no pool of cold air. At this point you can take water out of the stream for washing up your dishes.
Optimal is a little lake not far away for swimming of course.
The spots that look like this you visit for a day hike, look at the surrounding area and if there is a thick hedge approximately 100 metres away from the forest for wind protection of your camp. The 100 metres distance you need to avoid risks of forest fires.
It's worth to look in the laws about that if you have a different distance that's important for you.
Take photos of the spot if you like it, ask in the next village who owns it and simply ask the owner for permission to camp there.
After a few trials you will surely have success somewhere. It's worth the effort only for optimal wild camping spots.
In Germany we have no problem to find like this permission for a 80 persons boy scout camp with 11 camp fires.
I can't imagine that it is much different in Britain. And if you offer the farmer a bit help to work in the forest and hedge they surely aren't all strictly against it.
