On January 10th 2016, Clarkson came clean in his article in the Mail on Sunday and admitted that the whole thing was rigged. Clarkson wrote,

    “You may remember: I drove it (the Reliant Robin) around Sheffield and it kept falling over. Well now’s the time to come clean. A normal Reliant Robin will not roll unless a drunken rugby team is on hand. Or its windy. But in a headlong drive to amuse and entertain, I’d asked the backroom boys to play around with the differential so that the poor thing rolled over every time I turned the steering wheel”

https://www.reliant.website/topgear.shtml

IIRC they also put a big metal plate in the roof to make it even more top-heavy

And yet, several of my friends located the general Sheffield area agree that while the video was a bit over the top, generally, Robins tended to do that. That Sheffield is a surprisingly hilly city with sometimes hard turns meaning you have auto-acceleration on hills down, and often are a bit faster than you'd like, probably doesn't help either.