As someone who lives and walks extensively in the Chilterns, I can assure you that there are countless places that are ideal for a one-night wild camp. Here's what you do:
1 Plan your route from the appropriate Explorer map.
2 Towards evening, keep an eye open for a suitable pitch, preferably the edge of a field or in a grassy woodland clearing away from the path and nowhere near any habitation. Select a site where your tent is unlikely to be seen. If you choose a field, ensure that no animals are pastured in it.
3 When it starts to get dark, pitch your tent.
4 Wake at first light and strike camp.
5 Ensure that you have left no trace of your camp except for the outline of the footprint of your tent.
6 Walk for a mile or so and then have your breakfast.
7 I've never been caught in sixty years of wild camping but if you re discovered, don't argue, just apologize and move on.