Mine does the same on one specific hump in the road that I would go through at 40mph usually. The answer has been to gently slow down to 30 while approaching the obstacle and then speed up again. Problem solved!

As stated. Vehicle has had a replacement engine (112k) and new Borg & Beck clutch. Tyres are as new, well worth a look if you want a 5 door SE. https://ebay.us/m/vd13M8

My 1st gear switch connector hadn’t been fully pushed home, probably because of a small piece of grit. Cleaned it all and like you, voila! HDC works perfectly.

We'll have a small wager on dodgy earth or dirty contacts ...

Just to finish this off, the battery-disconnect-reset worked OK, And the radio was fine (no code needed), but after a week and a short drive with the rear window open, the cab switch for the rear window went awol again. I repeated the reset which...

@Kerlaan Once I'd worked out where the switch was, I found nothing connected to it. There was a connector tucked neatly out of the way behind some fittings on the body nearby that fitted, so I tried it out and the system works perfectly now...