Speaking as an extremely practical, least fanciful, and no-nonsense person, I must post that, yes, I did see two things I cannot explain. Bit complicated to write but I can still picture this in my mind's eye.
In car. Turned off A.41 towards home at Aston Clinton, happened to glance towards our children's little school and there, way above in the sky and small enough to be impossible to see clearly but sharp enough to be noticeable, I saw something unlit (not shiny), and stationary. Didn't think much at first, as assumed a plane at the kind of angle where it's difficult to see travel and direction. Looked back; still there, looked again just in time to see it shoot away upwards. Never saw anything move in that fashion before, nor since. To clarify, all this happened in the short time I drove (very slowly), from the main road then past the school. Still creepy to me.
The only other time I've seen anything remotely unusual was when we lived on the side of a Herefordshire hill, perched up high and overlooking a long stretched out valley. Just chanced to look at the sky in time to see an oval light, massive, in the sky over the valley. It quickly dimmed to nothing. It was way too big to be plane lights, fireworks (it was broad daylight), a flare, lightning, or any other day-to-day cause. It was eye-shaped and to this day I still joke that I have seen Gods' eye. I imagine this was what is known as fireball. Similar pictures on google images.