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The broadcaster owns 1,000 acres of land in the Cotswolds, and his attempt to farm it is the subject of new Amazon Prime Video series Clarkson's Farm.
The show has proven to be a hit, and over the weekend fans swarmed to Clarkson's Diddly Squat Farm Shop, causing huge queues to form in the village of Chadlington.
The Mirror reported that word got out that Clarkson was at the farm and people headed there in their thousands, dismaying local residents.
One local wrote on a community Facebook page: "Avoid going anywhere near Diddly Squat Farm Shop, whole road is blocked again, but worse there are people stopping on the 60mph bend with nowhere to go."
Another commented: "I've just seen pictures that someone else has posted. Utterly ridiculous.
"Clarkson needs to do something and quickly. It's going to cause an accident! Queues all up Burford Road."
The queues were such that emergency services were called on Saturday. However, Thames Valley Police said no crime had been committed.
A spokesperson shared a statement with LADbible, which read: "Officers received reports [on Saturday] in relation to congestion on the roads in Chadlington.
"Officers attended the scene, but no crime had been committed.
"Our neighbourhood team for the area is aware of the situation."
On Friday (18 June), Clarkson said he was 'genuinely amazed' by the response to the show and his bees are struggling to keep up with the demand for honey at his shop.
Writing on Twitter, he said: "I'm genuinely amazed at the response to Clarkson's Farm. Thank you all so much for your kind words.
"A big thank you too to everyone who's been to our little farm shop. The bees can hardly keep up with demand for their honey."
The current success at the farm strikes a markedly different tone to much of the show, which centres around money-making struggles, successive misfortunes and Clarkson's ineptitude. The 61-year-old is the first to admit that he hasn't a clue what he's doing when it comes to farming.
He told LADbible: "It's like when I lift the bonnet on a car. It's all just witchcraft, I have no idea what's going on.
"If I put you on a farm and said, 'Right, run that,' nobody has a clue. You go and buy a loaf of bread, you have no idea, no idea how it was made. None of us do... Definitely a fish out of water is what I was."
You can read more about the series - and why Clarkson won't be growing weed on his farm - here.
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