After saying in the OP that sundogs are more common than rainbows, I've been keeping a look out for them!
Okay, I'm outside more on showery days (good for rainbows) than I am just after sunrise on cold sunny mornings (good for sundogs) but I'm going to admit that my OP claim was wrong (for the UK anyway) as I'd not seen a good sundog since the OP until this week.
But on Tuesday morning, driving down the M40 to London at about 6:45 am, there was a beauty!
Only on one side of the sun, but it was really clear. I didn't risk trying to photograph it while I was driving though, and by the time I got to the motorway service station where I could stop, it had gone.