"Chappers",I have seen these many times.They can sometimes catch you unawares when you're looking skyward.I've also seen some strange white lights,like the ones you described but at a much lower level that seemed to have a ping-pong effect:traversing the sky then meeting with another light and repelling it away.This went on for thirty minutes.Couldn't explain it.My brother saw it too.
After all that,I can't explain what you've witnessed but just thought I'd let you know-you are not alone.